arXiv CSopen access

Exposure Bias Can Alleviate Itself via Directional and Frequency Rectification in Flow Matching

Exposure Bias Can Alleviate Itself via Directional and Frequency Rectification in Flow Matching Guanbo Huang1,2∗,‡ , Jingjia Mao1,2∗,‡ , Fanding Huang1∗ , Fengkai Liu1 , Xiangyang Luo1 , Yaoyuan Liang1 , Jiasheng Lu2 , Xiaoe Wang2 , Pei Liu2 , Ruiliu Fu2† , Ruqi Huang1† , and Shao-Lun Huang1†

arXiv:2606.28226v1 [cs.CV] 26 Jun 2026

1

Tsinghua Shenzhen International Graduate School, Tsinghua University 2 Central Media Technology Institute, Huawei

Abstract. Flow Matching (FM) has achieved remarkable generative performance, yet it suffers from exposure bias due to discrepancies between training and inference. Existing mitigation strategies typically rely on static constraints or external heuristics. In this work, we propose that exposure bias itself inherently contains dynamic signals that can guide its own rectification. To leverage this, we introduce DEFAR (DirEctional-Frequency Adaptive Rectification). This framework simulates the single-step inference process during training to identify exposure bias. It utilizes the directional and frequency adaptive feedback signals in bias itself to enhance the bias tolerance of the model. It consists of two key components: (1) Anti-Drift Rectification (ADR). ADR treats inference-time drift as a signal to learn the direction to steer deviated states back toward the target. ADR endows the model with intrinsic active self-rectification capabilities; (2) Frequency Compensation (FC). Empirically, we observe that accumulated bias often stems from a lack of low-frequency components in high-noise stages and exposure bias carries the missing frequency. FC leverages the bias itself as a self-feedback weighting factor to reinforce the missing frequency components. Experiments on CIFAR-10, CelebA-64, and ImageNet-256/512 show that DEFAR outperforms prior baselines and further demonstrates favorable scalability, compatibility, and inference robustness. Code will be made available in https://github.com/wuliwuliy/DEFAR. Keywords: Exposure bias · Flow matching · Adaptive rectification

1

Introduction

Recently, Flow Matching (FM) [2, 35, 36] has emerged as a promising framework for generative modeling. By modeling continuous-time flows, FM offers a more direct and efficient training paradigm compared to traditional diffusion-based Equal contributions. Corresponding authors: Ruiliu Fu, Ruqi Huang and Shao-Lun Huang. ‡ This work was conducted during the internship at Central Media Technology Institute, Huawei. ∗ †

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G. Huang, J. Mao, F. Huang et al.

approaches [19, 53, 55]. Its strong empirical performance and theoretical simplicity have established FM as a foundational method across diverse generation tasks, including image, video, and audio generation [5, 10, 23, 30, 40, 57, 60]. However, FM models remain inherently vulnerable to exposure bias, a fundamental challenge stemming from the discrepancies between training and inference inputs. As illustrated in Fig. 1, during training, the model is conditioned on perturbed input, namely a mixture of Gaussian noise and ground-truth data. The model effectively learns to predict the vector field without predicted error accumulation. In contrast, during multi-step inference, the model must exclusively rely on its own previous predictions. This propagates and accumulates the potential predicted error at each inference step. This forces the model to operate in the unexplored data space compared to the training stage where its predictive capability significantly degrades, ultimately leading to substantial deviation from the target distribution. While prior research has explored this issue within the DDPM framework [12, 31, 32, 42, 66], existing so𝒗! (𝒙𝒕 , 𝒕) lutions predominantly rely on static alignment strategies or exogenous noise injection. Some approaches in(i) During Training troduce inference-time regularization without altering the training pro𝒗! (' 𝒙𝒕, 𝒕) cess [31, 42, 66], while others attempt to mitigate bias during training by simulating potentially imperfect inference. For instance, IP [43] injects Data Noise (ii) During Inference fixed perturbations into training input data, and SS [8] directly re- Fig. 1: Illustration of exposure bias in places perturbed samples with pre- Flow Matching. (i) During training, the model is conditioned on perturbed inputs dicted samples. These methods gensampled strictly along the ideal linear path erally enforce a static alignment with (blue arrows). (ii) During inference, the inthe original ground truth or rely on put suffers from accumulated errors genexternally fixed noise augmentation to erated by previous steps, causing trainingimprove robustness. Notably, [47] pro- inference mismatch (purple arrows). poses Multi-step Denoising Scheduled Sampling (MDSS) and Single-step Denoising Scheduled Sampling (SDSS), which focus on passively enhancing the model’s robustness to input deviations. By exposing the model to perturbed states, MDSS encourages stability against accumulated errors but generally enforces a fixed alignment target regardless of the deviation’s severity. In this work, we advance beyond passive robustness to establish a dynamic correction mechanism. We empower the model to learn adaptive correction signals that are modulated by the severity of exposure bias.

··· ···

Specifically, we investigate the intrinsic properties of exposure bias from both directional and frequency perspectives. First, we simulate the inference process during training to expose drift. After inference, the exposure bias is inherently

DEFAR for Exposure Bias Alleviation.

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carried in the inferred state. And the simulation enables us to explicitly characterize the deviation from the state to the target endpoint. Building on this, we introduce a directional regularizer. This term acts as a steering force, guiding the model to rectify the deviated state back towards the target endpoint. This allows us to actively adjust the rectification magnitude according to the severity of the exposure bias itself. Second, identifying that exposure bias stems from prediction imperfection, we conduct a frequency analysis and observe a distinct deficiency in low-frequency components during the early denoising outputs from the model. Since these components encode critical structural information, their absence exacerbates error propagation. To quantify this, we introduce two metrics: Predicted Frequency Ratio (PFR), which measures the ratio of low-to-high frequency energy in prediction outputs, and Frequency Emphasis of Loss (FEL), which evaluates the relative focus of the loss function on different frequency bands. Intriguingly, we observe that exposure bias itself exhibits a complementary characteristic in relatively early high-noise timesteps: it naturally highlights neglected low-frequency regions. This motivates us to use the bias as a dynamic reweighting signal to mitigate itself. Building on these insights, we propose DEFAR (DirEctional-Frequency Adaptive Rectification), a flexible framework that leverages the dynamic nature of exposure bias itself to adaptively rectify FM models. DEFAR comprises two core components: (1) Anti-Drift Rectification (ADR): Functioning as a regularizer to the original training objective, ADR constructs a direction that explicitly steers the model from the deviated state back towards the target data distribution, actively correcting the prediction drift based on the severity of exposure bias itself. (2) Frequency Compensation (FC): Applied to the original training objective, FC utilizes the exposure bias itself as a reweighting signal to enhance the learning of missing low-frequency components via a negative feedback loop. Our main contributions are summarized as follows: – We propose Anti-Drift Rectification (ADR), a method that actively provides directional correction, endowing flow matching with superior resistance to bias compared to static alignment methods. – We identify the connection between exposure bias and missing low-frequency information, proposing Frequency Compensation (FC) to dynamically reinforce structural learning by leveraging the bias signal itself. – We integrate ADR and FC into a unified framework, DEFAR. Extensive experiments on CIFAR-10, ImageNet-256/512, and CelebA-64 demonstrate that DEFAR significantly outperforms existing baselines, while exhibiting scalability, architectural compatibility, and inference robustness.

2

Related Work

Exposure Bias. Exposure bias arises from the mismatch between training and inference inputs in sequential models [4, 46, 51, 61, 71, 72]. Among early approaches, DAD [59] combines ground truth and predicted tokens during training, and SS [8] samples biased inputs to better approximate inference. In diffusion

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G. Huang, J. Mao, F. Huang et al.

models, DDPM-IP [43] first formalizes exposure bias and perturbs training samples to simulate it. EP-DDPM [32] studies error propagation and introduces a cumulative-error regularizer. AE-DDPM [69] mitigates exposure bias via prompt learning, and MCDO [65] imposes manifold constraints. Inspired by distribution adaptation methods [21,22,70], training-free techniques include a time-shift sampler (TS-DDPM [31]), noise scaling (ES-DDPM [42]), training-distribution leak signals exploitation [12] and frequency-domain analysis with wavelet-based regularization [66]. Among prior works, MDSS/SDSS [47] is most relevant to our approach. It simulates multi- or single-step inference trajectories during training but persists in aligning predictions with the static ground-truth target. Consequently, this strategy merely bolsters the model’s passive robustness against input perturbations, failing to equip it with the capability to actively rectify accumulated errors. In contrast, we investigate the intrinsic signal properties of exposure bias in Flow Matching and introduce a novel paradigm that leverages the bias itself to drive active self-rectification. Reweighting loss for emphasizing salient area alignment. Several works explore reweighting strategies in loss functions to emphasize salient or informative regions, guiding models to focus on the most influential areas. In decomposable or multi-stage generation, Decomposable Flow Matching [17] applies spatially varying masks to highlight critical regions on outputs. In video generation, Proteus-ID [68] and MotiF [62] adopt motion-aware weighting to prioritize frequently moving regions. MotionCharacter [13] further improves learning efficiency by emphasizing motion-sensitive areas. Beyond spatial analysis, Latent Wavelet Diffusion [52] performs frequency analysis and reweights loss to concentrate learning on frequency dominant components. Together, these methods demonstrate that adaptive loss reweighting can effectively direct model capacity toward salient regions, improving robustness and representation efficiency.

3

Preliminaries

3.1

Flow Matching

We adopt the standard Flow Matching formulation [35], where time t ∈ [0, 1] drives the flow from the source noise ϵ ∼ N (0, I) at t = 0 to the target data x∗ ∼ pdata (x) at t = 1. A sample at time t is constructed as \label {eq:fm_path} \mathbf {x}_t = a_t \mathbf {x}_* + b_t \pmb {\epsilon },

(1)

where at and bt are predefined schedules. The corresponding conditional velocity t is given by the time derivative of the path: vt = a′t x∗ + b′tϵ , where a′t = da dt and dbt ′ bt = dt . FM trains a neural network vθ (x, t) to approximate this conditional velocity by minimizing \label {eq:fm_loss} \mathcal {L}_{\text {FM}}(\theta ) := \mathbb {E}_{\mathbf {x}_*, \pmb {\epsilon }, t} \!\left [ \big \| \mathbf {v}_{\theta }(\mathbf {x}_t, t) - (a'_t \mathbf {x}_* + b'_t \pmb {\epsilon }) \big \|^2 \right ].

(2)

This objective encourages the model to learn a time-dependent velocity field that consistently transports the intermediate distribution towards the true data

DEFAR for Exposure Bias Alleviation.

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distribution. For instance, to ensure the flow follows Optimal Transport (OT), we can employ the straight-line schedule at = t and bt = 1 − t, which simplifies the target velocity to a constant x∗ − ϵ along the linear path. 3.2

Fourier Frequency Analysis

The Fourier transform provides a way to represent spatial-domain signals in the frequency domain, decomposing them into sinusoidal components of different frequencies and amplitudes. Since the predicted velocity field v ∈ RH×W shares a similar spatial structure with images, we can directly apply frequency-domain analysis to it. The 2D Discrete Fourier Transform (DFT) of v is defined as: \label {eq:dft} \begin {split} \mathbf {V}(u,v) = \sum _{x=0}^{H-1} \sum _{y=0}^{W-1} \mathbf {v}(x, y)\, e^{-i 2\pi \left ( \frac {ux}{H} + \frac {vy}{W} \right )}, \end {split}

(3)

√ where (u, v) denotes the frequency coordinates, and i = −1 is the imaginary unit. The resulting V(u, v) consists of a real part R(V) and an imaginary part I(V), from which the amplitude and phase spectra can be derived as: \label {eq:amp_phase} \begin {split} |\mathbf {V}(u,v)| &= \sqrt { R(\mathbf {V})^2 + I(\mathbf {V})^2}, \\ \angle \mathbf {V}(u,v) &= \arctan \!\left (\frac {I(\mathbf {V})}{R(\mathbf {V})}\right ). \end {split} (4)

The inverse Fourier transform reconstructs the spatial-domain signal from its frequency representation: \label {eq:idft} \begin {split} \mathbf {v}(x,y) = \frac {1}{HW}\! \sum _{u=0}^{H-1}\sum _{v=0}^{W-1} \mathbf {V}(u,v)\, e^{i 2\pi \left ( \frac {ux}{H} + \frac {vy}{W} \right )}. \end {split}

(5)

In practice, we adopt the Fast Fourier Transform (FFT) and its Inverse (IFFT) for efficient computation. 3.3

Exposure Bias Problem Formulation

Exposure bias is a well-documented phenomenon in generative sequence modeling [4, 46] and has been recently investigated within diffusion-based frameworks [43, 47]. In the context of Flow Matching (FM), this issue manifests as a critical discrepancy between the training and inference phases. Specifically, during training, the model vθ (xt , t) relies on inputs xt derived from a linear interpolation between the true data distribution x∗ and Gaussian noise ϵ (Eq. 1). Conversely, during inference, the input x̂t is generated recursively from previous predictions, inevitably accumulating errors. This mismatch induces a distribution drift between the training state vθ (xt , t) and the inference state vθ (x̂t , t), which propagates through timesteps and progressively degrades sample quality. To explicitly model this effect during the training phase, we simulate the generation process to capture the resulting drift. As illustrated in Fig. 2, we

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G. Huang, J. Mao, F. Huang et al. Ground Truth Vel. Predicted Vel. (𝒗𝒕) Biased Vel. (𝒗 (𝒕) Anti-Drift Vel.

ADR

Bias

𝒙 (𝒕 (biased input) 𝒙𝒕

$𝒕𝟎,𝒕𝟏 − 𝒗𝐀𝐃𝐑 𝒗

FC

𝜹

𝒗𝒕𝟎 − 𝒗𝒈𝒕 𝝐 (𝒕=0)

𝒙𝒕𝟎 (𝒕𝟎) MSE (ℒ FC)

×

𝒙∗ (𝒕=1)

𝒙𝒕𝟏 (𝒕𝟏) MSE (ℒ ADR)

Fig. 2: Overview of DEFAR. (a) Anti-Drift Rectification: Introduces a learning target that actively guides the model from the drift-affected distribution back toward the data distribution. (b) Frequency Compensation: Reweights the original objective using exposure bias as a negative-feedback signal to mitigate low-frequency deficiency at relatively high-noise timesteps (e.g., t0 ). Together, DEFAR adaptively rectifies exposure bias across both directional and frequency dimensions by leveraging the bias signal itself.

incorporate a one-step inference simulation in the training loop. At time t0 , given the ideal perturbed input xt0 , the model predicts the velocity vθ (xt0 , t0 ). Due to unavoidable prediction errors, the estimated velocity naturally deviates from the ground-truth direction. Proceeding to the next timestep t1 , the resulting state is computed as: \hat {\mathbf {x}}_{t_0,t_1} = \mathbf {x}_{t_0} + (t_1 - t_0) \cdot \mathbf {v}_{\theta }(\mathbf {x}_{t_0}, t_0). (6) This estimated state carries the prediction drift. Consequently, the subsequent velocity vθ (x̂t0 ,t1 , t1 ) exacerbates the deviation from the previous step. Based on this simulation, we operationalize exposure bias at a single timestep to guide our training. We formulate the bias for any timestep interval t0 , t1 as: \label {eq:exposure_bias} \pmb {\delta }_{t_0,t_1} = \mathbf {v}_{\theta }(\hat {\mathbf {x}}_{t_0,t_1}, t_1) - \mathbf {v}_{\theta }(\mathbf {x}_{t_1}, t_1).

(7)

This formulation quantifies the variation in predicted velocity caused solely by replacing the ideal input xt1 with the drift-affected input x̂t0 ,t1 , serving as a tractable proxy for the actual inference discrepancy.

4

DirEctional-Frequency Adaptive Rectification

This section presents our method, DEFAR, a framework designed to adaptively mitigate exposure bias by leveraging the intrinsic directional and frequency signals of the bias itself. As illustrated in Fig. 2, our approach comprises two core components: Anti-Drift Rectification (ADR) and Frequency Compensation (FC), detailed in Sec. 4.1 and Sec.4.3 respectively, with Sec.4.2 providing the metrics used for the subsequent frequency analysis. ADR operates in the directional dimension, actively learning a restorative direction to steer drifted states back toward the target endpoint based on the severity of the bias. In parallel, FC functions in the frequency dimension, leveraging the frequency signature of the bias as a self-feedback cue to adaptively compensate for deficient low-frequency components during high-noise timesteps. By integrating them into the unified DEFAR framework, these two mechanisms complement each other, bolstering

DEFAR for Exposure Bias Alleviation.

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the bias tolerance of the model to training-inference mismatch from both directional and frequency dimensions. The learning objective combines the two mechanisms as follows: \label {eq:all_methods} \mathcal {L} := \beta _1 \mathcal {L}_{\text {\ourdri {}}} + \beta _2 \mathcal {L}_{\text {\ourfre {}}},

(8)

where β1 and β2 are weighting coefficients for ADR and FC, respectively. LFC represents the LFM reweighted by exposure bias signal. DEFAR thus offers an effective solution to alleviate exposure bias by exploiting the informative signals inherent in the bias itself. The training procedure is summarized in Algorithm 1. 4.1

Anti-Drift Rectification (ADR)

As formulated in Sec. 3.3, exposure bias emerges from the recursive accumulation of prediction errors, integrating drift into x̂t0 ,t1 . When existing Flow Matching frameworks process such biased states, they typically impose a static optimization objective [47], which lacks sensitivity to the dynamically varying severities of prediction drift. To empower the model with active resistance, we introduce Anti-Drift Rectification (ADR), a mechanism that turns the exposure bias into an endogenous control signal to mitigate itself. Our fundamental motivation is grounded in the invariance of the target data distribution. Regardless of the severity of the accumulated exposure bias, the ground-truth endpoint x∗ remains deterministic. This invariance allows us to establish a dynamic anchor: the anti-drift target velocity vADR = a′t1 x∗ + b′t1 x̂t0 ,t1 . This vector acts as a restorative trajectory, originating strictly from the current biased state and guiding toward the target distribution. By leveraging this anchor, the model is empowered to actively recognize the precise corrective direction required to navigate back to the target manifold, adapting seamlessly to varying degrees of exposure bias. To enable the model to learn this rectifying direction, we introduce ADR as a regularization term appended to the standard FM objective (which will be further upgraded to our FC objective in Sec. 4.3). Notably, when no exposure bias occurs, vADR naturally degenerates to align parallel to a′t1 x∗ + b′t1 ϵ . This guarantees consistency with the original probability flow, ensuring that the regularization only actively penalizes trajectory drift without perturbing optimal predictions. The ADR regularization term is formulated as follows: \label {eq:adr_loss} \begin {aligned} \mathcal {L}_{\text {\ourdri {}}} &= \mathbb {E}_{\mathbf {x}_*, \hat {\mathbf {x}}_{t_0,t_1}, t_0,t_1} \left [ \left \| \frac {\mathbf {v}_{\theta }(\hat {\mathbf {x}}_{t_0,t_1}, t_1)}{\|\mathbf {v}_{\theta }(\hat {\mathbf {x}}_{t_0,t_1}, t_1)\|_2} - \frac {a'_{t_1} \mathbf {x}_* + b'_{t_1} \hat {\mathbf {x}}_{t_0,t_1}}{\|a'_{t_1} \mathbf {x}_* + b'_{t_1} \hat {\mathbf {x}}_{t_0,t_1}\|_2} \right \|^2 \right ]. \end {aligned}

(9)

This design serves as a dynamic self-rectifying mechanism: the regularization gradient is intrinsically proportional to the angle of deviation. As the exposure bias exacerbates the drift, the angular discrepancy widens, automatically amplifying the rectification signal. Through this dynamic modulation, ADR forces the model to actively learn a restorative direction, thereby alleviating sampling error and dismantling the cycle of recursive error propagation, thus enabling the model to leverage the exposure bias signal to mitigate the bias itself.

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4.2

G. Huang, J. Mao, F. Huang et al.

Frequency Analysis Metrics

Recent studies [31,42,66] attribute exposure bias to the distributional mismatch between training and inference predictions. While ADR effectively rectifies the geometric direction of this drift, the internal structure of exposure bias, specifically its frequency characteristics, remains underexplored. In this section, we analyze this pixel-level frequency mismatch and propose a fine-grained compensation strategy derived from the exposure bias itself. Inspired by the frequency analyses in [34, 56], we introduce two metrics to quantify the frequency distribution of velocity and loss for further analysis: the Predicted Frequency Ratio (PFR), which measures the ratio of low-to-high frequency energy in prediction, and Frequency Emphasis of Loss (FEL), which evaluates the relative focus of the loss function on different frequency bands. We first introduce the computation of PFR. Specifically, given the predicted velocity v ∈ RH×W produced by the FM model, we perform a 2D FFT on it: \label {eq:fft} \begin {split} \mathbf {V}(u,v) = \text {FFT}(\mathbf {v}(i,j)). \end {split}

(10)

To investigate the proportion of low- and high-frequency bands, we apply Low-Pass Filter (FLP ) and High-Pass Filter (FHP ) defined as: \label {eq:filters} \begin {split} \mathbf {F}_{\text {LP}}(u,v) = \mathbb {I}\left [ D(u,v) \leq D_{\text {cutoff}} \right ], \quad \mathbf {F}_{\text {HP}}(u,v) = \mathbf {1} - \mathbf {F}_{\text {LP}}(u,v), \end {split} (11) √ where D(u, v) = u2 + v 2 is the frequency magnitude and Dcutoff is the cutoff frequency. We compute the energy ratio between the low- and high-frequency components and define PFR as follows: \label {eq:energy_ratio} \begin {split} \text {PFR} := \frac {\sum _{u,v} ||\mathbf {V}(u,v)||^2 \cdot \mathbf {F}_{\text {LP}}(u,v)} {\sum _{u,v} ||\mathbf {V}(u,v)||^2 \cdot \mathbf {F}_{\text {HP}}(u,v)}. \end {split}

(12)

We then define the FEL. Here, we consider the target velocity map vtarget ∈ RH×W (typically the standard FM target velocity) and the MSE loss map L ∈ RH×W . To compute it, we divide vtarget into high- and low-frequency regions. The magnitude of the loss map L in each region reflects the relative emphasis of loss. Thus, we separately sum the loss values within the low- and high-frequency regions to quantify how the loss distributes its emphasis across different frequency components. This metric further serves as an indicator of the capability of loss to compensate for frequency discrepancies. We first apply Eq. 10 and 11 to perform the FFT of vtarget and compute the corresponding low- and high-frequency masks in the frequency domain. These masks are then used to separate vtarget into its low- and high-frequency components, which are subsequently transformed back to the spatial domain via IFFT. Finally, we compute the salient low- and high-frequency region masks in the spatial domain by thresholding the corresponding values according to their percentile distributions. \label {eq:ifft_masks} \begin {split} \mathbf {v}_{\text {low}} &= \text {IFFT}(\mathbf {V} \cdot \mathbf {F}_{\text {LP}}), \quad \mathbf {v}_{\text {high}} = \text {IFFT}(\mathbf {V} \cdot \mathbf {F}_{\text {HP}}),\\ \mathbf {M}_{\text {LFR}}(i,j) &= \mathbb {I}\big [\mathbf {v}_{\text {low}} > p(\mathbf {v}_{\text {low}})\big ], \quad \mathbf {M}_{\text {HFR}}(i,j) = \mathbb {I}\big [\mathbf {v}_{\text {high}} > p(\mathbf {v}_{\text {high}})\big ], \end {split}

(13)

DEFAR for Exposure Bias Alleviation. Motivation

(a) PFR of Model Prediction

9

Implementation

(b) PFR of Exposure Bias

(c) Exposure Bias Emphasis at high-noise timestep

(d) Relative improvement in FEL

Fig. 3: Motivation and Verification of FC. (a) illustrates frequency trends derived from forward-perturbed inputs, while (b) reveals contrasting trends using inputs generated via single-step inference. In (b), for any starting timestep t0 , the exposure bias PFR is averaged over all subsequent sampled timesteps t1 ∈ (t0 , 1], capturing the cumulative impact across varying inference intervals. (c) visualizes the heatmap of exposure bias at high-noise timesteps, focusing on low-frequency semantics. (d) shows that the reweighted loss effectively emphasizes low-frequency regions during high-noise timesteps. The continuous time horizon [0, 1] is discretized into 50 uniform timesteps. The metrics are averaged across 50, 000 samples from ImageNet-256 on SiT-B/4.

where p(·) denotes a percentile threshold function, vlow and vhigh represent the low- and high-frequency components of vtarget . The resulting masks, MLFR and MHFR , indicate the low- and high-frequency region masks, respectively. Finally, we compute FEL as follows: \label {eq:R_LFDL} \begin {aligned} \text {FEL} &:= \frac {\sum \tilde {\pmb {\mathcal {L}}} \cdot \mathbf {M}_{\text {LFR}}} {\sum \tilde {\pmb {\mathcal {L}}} \cdot \mathbf {M}_{\text {HFR}}}, \quad \text {where} \quad \tilde {\pmb {\mathcal {L}}}^{(i,j)} = \frac {\pmb {\mathcal {L}}^{(i,j)}} {\sum _{i=1}^{H} \sum _{j=1}^{W} \pmb {\mathcal {L}}^{(i,j)}}. \end {aligned}

(14)

The trend of FEL reveals how the loss distributes attention across low- and high- frequency regions during training. 4.3

Frequency Compensation (FC)

Leveraging the PFR metric proposed in Sec. 4.2, we analyze the forward perturbation process and identify that prediction drift is primarily attributed to a frequency deficiency, which subsequently induces exposure bias. Exposure bias intrinsically compensates for the low-frequency deficiency during high-noise timesteps. As visualized in Fig. 3 (a), the model prediction exhibits a distinct frequency shift over time. During the early highnoise steps (t → 0), the prediction is characterized by a lack of low-frequency content (indicated by low PFR values) compared to the target vtarget . Conversely, Fig. 3 (b) reveals that the exposure bias follows an inverse trend, exhibiting high PFR values in this phase. This uncovers a complementary relationship: the exposure bias encapsulates the low-frequency structural components that the model inherently struggles to capture initially. Exposure bias serves as a dynamic and self-decaying corrective signal. When approaching low-noise (t → 1), the model progressively reconstructs sufficient low-frequency content. Concurrently, the low-frequency dominance within the exposure bias autonomously diminishes. This prevents excessive structural compensation, transforming the exposure bias from a static error into a dynamically weighted variable for self-correction.

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Algorithm 1 DEFAR: Training 1: Input: model f to predict velocity with parameters θ, dataset D, learning rate η, ADR loss weight β1 , FC loss weight β2 , normalization coefficient α, path interpolation coefficients at , bt (with derivatives a′t , b′t ) and stability constant ξ. 2: While θ not converged do 3: ϵ ∼ N (0, I), x∗ ∼ D, t0 , t1 ∈ [0, 1], and t1 > t0 4: xt0 ← t0 x∗ + (1 − t0 )ϵϵ, xt1 ← t1 x∗ + (1 − t1 )ϵϵ 5: vt0 ← fθ (xt0 , t0 ), vt1 ← StopGradient(fθ (xt1 , t1 )) // Single-step inference simulation 6: x̂t0 ,t1 ← xt0 + (t1 − t0 )vt0 7: v̂t0 ,t1 ← fθ (x̂t0 ,t1 , t1 ) // ADR target velocity 8: vADR ← a′t1x∗ + b′t1 x̂t0 ,t1  v̂t0 ,t1 ADR − ∥vvADR ∥v̂t0 ,t1 ∥2 ∥2

2

9:

LADR ← E

10:

δ t0 ,t1 ← v̂t0 ,t1 − vt1

11:

Wt0 ,t1 ← 1 + α PH PWt0 ,t1 (i,j) 2 δ i=1 j=1 ∥δ t0 ,t1 ∥ +ξ h
2i LFC ← E Wt0 ,t1 · vt0 − (a′t0 x∗ + b′t0 ϵ) L ← β1 LADR + β2 LFC θ ← θ − η∇θ L

12: 13: 14:

(i,j)

δ ∥δ

(i,j)

∥2

// ADR regularization loss

// Spatial frequency weights // FC-reweighted FM loss

The low-frequency content of exposure bias is semantically grounded in the target data. To verify that this complementary signal is not noise, we visualize the spatial distribution of the exposure bias in Fig. 3 (c). The heatmaps confirm that during the high-noise timesteps, the bias is concentrated on the lowfrequency structural regions of the original images (More samples in Appendix). These observations motivate our core insight: the dynamic frequency signatures of exposure bias constitute an endogenous feedback loop. This empowers the model to rectify low-frequency deficiencies using the bias signal, thereby reducing prediction errors and ultimately mitigating the bias itself. Inspired by [13, 52, 62, 68], which demonstrate that reweighting the loss can enhance saliency alignment, we design a negative-feedback weight mask for the original loss based on exposure bias. The weight is formally defined as: \label {eq:W_exp_BC} \begin {split} \mathbf {W}_{t_0,t_1}^{(i,j)} = 1 + \alpha \, \frac {\|\pmb {\delta }_{t_0,t_1}^{(i,j)}\|^2} {\sum _{i=1}^{H} \sum _{j=1}^{W} \|\pmb {\delta }_{t_0,t_1}^{(i,j)}\|^2 + \xi }, \end {split}

(15)

where α is a scaling coefficient, and ξ is a small constant introduced to ensure numerical stability. We then reweight the FM learning objective as follows: \label {eq:weighted_fm_loss} \begin {split} \mathcal {L}_{\text {\ourfre {}}} &:=\mathbb {E}_{\mathbf {x}_*,\,\pmb {\epsilon },t_0,t_1} \!\left [ \left \| \mathbf {W}_{t_0,t_1}\cdot \big ( \mathbf {v}_{\theta }(\mathbf {x}_{t_0},t_0) - (a'_{t_0} \mathbf {x}_* + b'_{t_0} \pmb {\epsilon }) \big ) \right \|^2 \right ]. \end {split}

(16)

This weighting strategy adaptively adjusts the loss distribution according to the exposure bias, emphasizing the missing frequency components. Exposure bias reweighting prioritizes low-frequency learning during high-noise timesteps. To quantitatively evaluate the impact of LFC , we analyze the FEL. Prior studies [3,20,26,33,38,64,73] indicate that the early generation phase, especially high-noise timesteps, is critical for establishing the global

DEFAR for Exposure Bias Alleviation.

11

structure of generated samples, which directly influences the final generation quality. Consistent with these findings, as illustrated in Fig. 3 (d), the exposurebias-reweighted loss exhibits a relative increase over the raw baseline, directing the learning focus toward low-frequency components during the high-noise phase (t → 0). By utilizing the bias signal to compensate for frequency deficiencies, FC translates the exposure bias into a corrective signal, thereby leveraging the bias to mitigate its underlying cause.

5

Experiments

5.1

Experiment Setting

Main Implementation. We evaluate our methods on conditional image generation tasks on ImageNet-256/512 [7] and CIFAR-10 [27], as well as unconditional tasks on CIFAR-10 and CelebA-64 [37]. Following prior works [15, 43], we generate 50K samples using 50 Number of Function Evaluations (NFE). CIFAR-10 and CelebA-64 are processed in pixel space, while ImageNet-256 is encoded in the latent space of a pre-trained VAE-ft-EMA tokenizer [48]. All models are trained from scratch on Ascend 910B NPUs, except that REPA, DDT and OTCFM experiments are conducted on A100 GPUs. Based on grid search results (detailed in Appendix), we set β1 = 10, β2 = 1 and α = 1 in all experiments. During training, all variants of our methods randomly select a pair of timesteps (t0 , t1 ) with t1 > t0 in each iteration. For ablation studies, we adopt SiT-B/4 as the default backbone and at = t, bt = 1 − t unless stated otherwise. For Discriminator Guidance (DG), we follow [24] and train a shallow U-Net discriminator for the SiT-B/4 score model with an ADM classifier. For mini-batch OT coupling, we follow [58] and report five-seed statistics. More details in Appendix. Evaluation Metrics. We report the training budget in NPU/GPU hours (GPU for REPA, DDT, and mini-batch OT coupling experiments), denoted as “Hour”. We follow [9] for the computation of all evaluation metrics. Fréchet Inception Distance (FID) [18] is reported as our primary metric, alongside sFID [41], Inception Score (IS) [50], Precision and Recall [29]. Following prior works [9,31,47], we utilize the full training sets of CIFAR-10 and CelebA-64, and the standard testset of ImageNet, as our reference distributions. Details in Appendix. Frequency Analysis Details. To maximize the separation between low- and high-frequency regions, the cutoff frequency is set to min(H, W )//8 in Eq. 11, with 20% and 25% thresholds respectively in Eq. 13. Baselines. We compare our method with four baselines: SiT [40], IP [43], SDSS [47], and MDSS [47]. For IP, SDSS, and MDSS, which were originally developed under the DDPM framework, we adapt their core ideas to the flow matching setting. Specifically, IP perturbs the input with additional noise to simulate inference, SDSS aligns predictions with the static target during singlestep inference in training, and MDSS performs multi-step inference (we use 4 steps as reported to achieve the best performance [47]). We further evaluate two complementary exposure-bias mitigation paradigms. DG [24] corrects generated states at inference time with external classifier and discriminator. Mini-batch

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Table 1: Quantitative comparison on conditional datasets. Class-conditional (without/with CFG following SiT [40]) generation on ImageNet-256 and CIFAR-10. All entries are reported using 50 sampling steps (NFE). Red highlights improvements by our method, and green indicates degradations compared to gray baseline. Under a comparable cost (e.g., 144h vs. 166h on ImageNet), DEFAR outperforms the baselines. ImageNet-256 (conditional) Method

Backbone Params

SiT (origin) [40]

SiT-B/4

IP [43] SiT-B/4 SDSS [47] SiT-B/4 MDSS (4steps) [47] SiT-B/4 DEFAR w/o FC DEFAR w/o ADR DEFAR

SiT-B/4 SiT-B/4 SiT-B/4

DEFAR

SiT-B/4

Iters Hour

FID↓

131M 500k 166 61.64/31.64 +0.0/+0.0 131M 500k 166 60.45/29.84 131M 500k 228 61.25/30.29 131M 500k 228 63.66/31.90

sFID↓ 12.20/8.44 +0.0/+0.0 12.49/8.80 13.23/8.95 14.38/10.05

IS↑

CIFAR-10 (conditional)

Pre.↑

Rec.↑

24.67/55.65 0.387/0.542 +0.0/+0.0 +0.0/+0.0 26.05/60.20 0.404/0.563 25.81/58.69 0.387/0.549 24.72/56.89 0.382/0.544

Iters Hour

0.581/0.524 +0.0/+0.0 0.578/0.523 0.588/0.534 0.583/0.527

FID↓

sFID↓

IS↑

Pre.↑

250k 11 14.09/9.36 6.28/5.73 8.22/8.90 0.617/0.676 +0.0/+0.0 +0.0/+0.0 +0.0/+0.0 +0.0/+0.0 250k 11 13.63/8.76 6.43/5.58 8.18/8.97 0.624/0.685 250k 15 13.27/8.27 5.97/5.41 8.21/8.91 0.612/0.679 250k 15 12.73/8.45 6.29/5.93 8.25/9.06 0.631/0.689

131M 500k 228 59.77/29.69 12.77/9.00 25.81/59.25 0.377/0.539 0.598/0.549 200k 131M 500k 289 57.17/28.71 10.65/8.25 26.55/60.43 0.398/0.557 0.590/0.532 200k 131M 250k 144 60.40/29.81 9.05/7.35 26.21/58.81 0.375/0.531 0.586/0.532 120k -1.24/ -1.83 -3.15/ -1.09 +1.54/+3.16 -0.012/-0.011 +0.005/+0.008 131M 500k 289 56.39/28.34 9.50/7.84 26.62/58.94 0.386/0.551 0.594/0.524 180k

Rec.↑ 0.538/0.500 +0.0/+0.0 0.539/0.500 0.550/0.506 0.529/0.484

12 11.61/7.62 6.07/6.21 8.30/9.05 0.599/0.669 0.556/0.507 16 11.25/7.53 5.71/5.53 8.30/9.10 0.601/0.677 0.557/0.506 10 12.01/7.73 5.46/5.13 8.27/9.01 0.605/0.667 0.555/0.514 -2.08/-1.63 -0.82/-0.60 +0.05/+0.11 -0.012/-0.009 +0.017/+0.014 15 11.22/7.56 5.32/5.21 8.31/9.06 0.618/0.682 0.553/0.500

Table 2: Unconditional generation and complementary mitigation strategies. Left: Quantitative results on unconditional CIFAR-10 and CelebA-64 (50 NFE), where DEFAR (120k) surpasses baselines under a comparable training budget. Right: Complementarity with two exposure-bias mitigation paradigms, DG on conditional ImageNet-256 and mini-batch OT coupling on unconditional CIFAR-10. Method

Backbone Params Iters

SiT (origin) [40]

SiT-B/4

IP [43] SiT-B/4 SDSS [47] SiT-B/4 MDSS(4steps) [47] SiT-B/4 DEFAR w/o FC SiT-B/4 DEFAR w/o ADR SiT-B/4 DEFAR SiT-B/4 DEFAR

SiT-B/4

CIFAR-10

CelebA-64

Hour FID↓ sFID↓ IS↑ Pre.↑ Rec.↑ Hour FID↓ sFID↓ IS↑

131M 250k 12 17.41 6.19 +0.0 +0.0 131M 250k 12 15.95 6.65 131M 250k 17 16.02 6.37 131M 250k 17 16.10 6.59

7.82 0.586 0.539 +0.0 +0.0 +0.0 7.97 0.583 0.556 7.70 0.590 0.542 7.91 0.594 0.547

131M 250k 17 15.92 6.45 7.83 0.585 0.554 131M 250k 23 15.99 5.99 8.07 0.580 0.562 131M 120k 11 15.93 5.99 7.86 0.567 0.567 -1.48 -0.20 +0.04 -0.019 +0.028 131M 250k 23 14.82 5.88 7.79 0.570 0.563

36 7.04 6.88 +0.0 +0.0 36 5.93 6.57 60 6.12 8.01 60 6.10 8.29

2.76 +0.0 2.72 2.71 2.91

Discriminator guidance [24] (conditional ImageNet-256 with SiT-B/4): Pre.↑ Rec.↑

Method

0.626 +0.0 0.640 0.671 0.623

SiT 61.64 12.20 24.67 0.387 0.581 +0.00 +0.00 DEFAR 60.40 9.05 26.21 0.375 0.586 -1.24 +1.54 SiT-G++ ADM/U-Netshallow 60.92 11.10 25.08 0.388 0.579 -0.72 +0.41 DEFAR-G++ ADM/U-Netshallow 59.03 8.84 26.49 0.374 0.590 -2.61 +1.82

0.521 +0.0 0.543 0.476 0.527

60 6.83 6.47 2.67 0.676 0.498 80 4.96 6.26 2.94 0.641 0.541 36 5.91 6.13 2.77 0.634 0.521 -1.13 -0.75 +0.01 +0.008 +0.000 80 4.53 6.41 2.92 0.629 0.551

Cls./Disc.

FID↓ sFID↓ IS↑ Pre.↑ Rec.↑ ∆FID ∆IS

Mini-batch OT coupling [58] (unconditional CIFAR-10): Method Backbone Hour Iters FID100 ↓ OT-FM OT-FM + DEFAR OT-CFM OT-CFM + DEFAR

U-Net U-Net U-Net U-Net

20 20 20 20

FID1000 ↓

Avg. FID↓

∆Avg. FID

400k 4.643±0.035 3.824±0.037 4.233±0.027 +0.000±0.000 200k 4.397±0.029 3.716±0.017 4.056±0.018 -0.177±0.023 400k 4.446±0.037 3.744±0.029 4.095±0.022 -0.138±0.033 200k 4.260±0.047 3.660±0.037 3.960±0.034 -0.273±0.029

OT coupling (OT-CFM) [58] changes the noise-data coupling during training to reduce transport-path variance. These two paradigms allow us to test whether DEFAR remains effective when exposure bias is also mitigated by inference-time correction or coupling-based path straightening. 5.2

Quantitative Experiments

To account for differences in computational environments, we reproduce the key baselines and report the results in Tab. 1 and Tab. 2. We highlight five primary findings: (i) Under comparable training budgets, DEFAR consistently improves upon the SiT baseline, reducing FID by 1.24/1.83 on ImageNet256 without/with Classifier-Free Guidance (CFG), 2.08/1.63 on conditional CIFAR-10, and 1.48 and 1.13 on unconditional CIFAR-10 and CelebA-64, respectively. This confirms its effectiveness in enhancing generation quality. (ii) ADR outperforms MDSS and SDSS [47]. Unlike these baselines, which rely on static alignment targets, ADR learns an active anti-drift target, validating the advantage of dynamic directional rectification. (iii) Both ADR and FC independently yield performance gains, while their integration within the unified DEFAR framework achieves better results. (iv) While prior methods passively mitigate exposure bias via fixed input perturbation (IP) or static target alignment (SDSS, MDSS), DEFAR actively rectifies prediction drift and compen-

DEFAR for Exposure Bias Alleviation. IP

SDSS

MDSS

DEFAR (ours)

ImageNet256×256

SiT

13

IP

SDSS

MDSS

ours

SiT

IP

SDSS

MDSS

ours

CelebA64×64

SiT

Fig. 4: Qualitative Comparison. DEFAR produces the most realistic samples on ImageNet-256 and CelebA-64. Red boxes highlight the blurriness or distorted details.

sates for deficient frequency components, achieving consistent empirical gains over these approaches. (v) In Tab. 2 (right), the DG and mini-batch OT comparisons further verify complementarity. For DG, DEFAR improves FID by 0.52 over DG alone, and combining DEFAR with DG reduces FID by 1.89, suggesting that DEFAR strengthens the base model during training while DG provides complementary inference-time guidance. For mini-batch OT coupling, combining DEFAR with OT-CFM achieves the best Avg. FID 3.960±0.034, outperforming OT-CFM alone by 0.135 and DEFAR alone by 0.096 in terms of the mean value. This suggests that OT-CFM reduces the transport-path difficulty and thereby provides a better basis for DEFAR to perform accurate fine-grained rectification according to the magnitude of exposure bias, leading to further gains. 5.3

Qualitative Experiments

All methods use the same random seed and 50 NFE for a fair comparison. As shown in Fig. 4, baselines exhibit two clear visual artifacts: (i) Rows 1, 2,

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Table 3: Scalability of DEFAR on ImageNet-256. 50-NFE generation (without/with CFG). DEFAR consistently outperforms SiT across different scales. ImageNet-256 Method Backbone Params Iters Hour SiT [40] DEFAR

SiT-B/4 SiT-B/4

131M 131M

500k 250k

DEFAR

SiT-B/4

131M

SiT [40] DEFAR

SiT-M/2 SiT-M/2

308M 308M

FID↓

sFID↓

IS↑

Pre.↑

Rec.↑

166 144

500k

61.64/31.64 12.20/8.44 24.67/55.65 60.40/29.81 9.05/7.35 26.21/58.81 -1.24/-1.83 -3.15/-1.09 +1.54/+3.16 289 56.39/28.34 9.50/7.84 26.62/58.94

0.387/0.542 0.581/0.524 0.375/0.531 0.586/0.532 -0.012/-0.011 +0.005/+0.008 0.386/0.551 0.594/0.524

700k 350k

311 330 661

30.57/8.23 10.90/6.13 58.66/154.71 0.547/0.750 0.654/0.531 29.46/7.85 5.60/4.64 59.01/156.27 0.549/0.751 0.639/0.518 -1.11/-0.38 -5.30/-1.49 +0.35/+1.56 +0.002/+0.001 -0.015/-0.013 27.58/7.30 7.35/4.96 62.09/159.76 0.546/0.752 0.658/0.531

DEFAR

SiT-M/2

308M

700k

SiT [40] DEFAR

SiT-XL/2 SiT-XL/2

675M 675M

700k 2260 350k 2300

DEFAR

SiT-XL/2

675M

25.85/5.88 7.63/4.73 68.93/183.58 0.570/0.762 0.659/0.541 24.93/5.74 5.71/4.71 71.63/188.75 0.580/0.775 0.651/0.532 -0.92/-0.14 -1.92/-0.02 +2.70/+5.17 +0.010/+0.013 -0.008/-0.009 700k 4640 18.45/4.14 6.34/4.95 77.80/199.59 0.621/0.810 0.644/0.529

Table 4: Architectural compatibility and sampling robustness. Left: Integration into REPA and DDT. 250-NFE generation under CFG, with and without DEFAR. Models are fine-tuned on ImageNet-512 from official ImageNet-256 checkpoints. Right: Generation across varying NFEs without CFG on ImageNet-256. ImageNet-512 Model

Params Iters Hour

FID↓ sFID↓

IS↑

Pre.↑ Rec.↑

REPA-XL/2 [67] 675M + DEFAR 675M

100k 400 3.99 11.76 248.60 0.796 0.595 45k 410 3.46 9.12 255.26 0.798 0.582 -0.53 -2.64 +6.66 +0.002 -0.013

DDT-XL/2 [63] + DEFAR

100k 570 1.90 4.33 281.25 0.793 0.601 45k 580 1.82 4.21 285.42 0.799 0.596 -0.08 -0.12 +4.17 +0.006 -0.005

675M 675M

SiT Steps

IP

SDSS

MDSS DEFAR(250k) DEFAR(500k)

FID↓ IS↑ FID↓ IS↑ FID↓ IS↑ FID↓ IS↑ FID↓

IS↑

FID↓

IS↑

63.63 24.70 61.25 26.21 63.41 25.80 65.93 24.78 61.12

25.62

57.20

25.84

50

61.64 24.67 60.45 26.05 61.25 25.81 63.66 24.72 60.40

26.21

56.39

26.62

100

60.42 24.48 58.26 26.01 59.92 25.78 61.33 24.64 58.11

26.09

55.89

26.51

250

59.84 24.30 57.75 25.83 59.23 25.64 61.33 24.48 57.56

25.91

55.66

26.33

500

59.70 24.24 57.58 25.76 59.06 25.56 61.10 24.41 57.32

25.79

55.60

26.30

30

and 5 exhibit severe structural disintegration and missing details. (ii) Rows 3, 4, and 6 show blurred object-background boundaries. These issues arise from the exposure bias accumulating during high-noise timesteps, causing confusion between the primary object and the surrounding context. In contrast, DEFAR generates images with more coherent structures and consistent textures.

6

Discussion

In this section, we conduct a multifaceted evaluation of DEFAR, assessing its scalability across model sizes, frequency restoration capability, and generalizability to diverse architectures and inference configurations. Scalability across Model Sizes. Tab. 3 reports FID alongside four metrics of DEFAR across different model scales (B/4, M/2 and XL/2). DEFAR consistently outperforms the SiT models and exhibits scalability in generative quality. Frequency Restoration Analysis. As shown in Fig. 5, we compare the PFR of predicted velocities between DEFAR and the SiT baseline when given forwardperturbed inputs. DEFAR effectively recovers low-frequency components during high-noise timesteps, alleviating the low-frequency deficiency. Universality across Architectures. We integrate our method into two strong and distinct diffusion transformers: REPA [67] (featuring representation align-

DEFAR for Exposure Bias Alleviation.

15

Table 5: Generalization across path interpolants and sampling methods. FID on unconditional CIFAR-10.

Fig. 5: Low-frequency Restoration. After comparable training, DEFAR can compensate for missing low-frequency components during high-noise timesteps (Red box).

Interpolant

Model

Linear Linear

SiT-B/4 DEFAR-B/4

12 11

17.41 16.81 15.93 15.31

SBDM-VP SiT-B/4 SBDM-VP DEFAR-B/4

12 11

19.89 18.89 18.33 17.35

12 11

17.31 16.42 15.84 14.91

GVP GVP

SiT-B/4 DEFAR-B/4

Hour ODE SDE

ment) and DDT [63] (featuring structural decoupling). We fine-tune their default REPA-XL/2 and DDT-XL/2 backbones on ImageNet-512 from the official ImageNet-256 pre-trained checkpoints. This demonstrates that our method seamlessly adapts to these advanced paradigms. As shown in Tab. 4 (left), under a comparable training budget, our approach consistently achieves superior generation quality. Adaptability to Path Interpolants and Sampling Methods. As shown in Tab. 5, we examine three interpolant types: Linear, SBDM-VP, and GVP [40]. The results indicate that DEFAR is adaptable to the choice of the forward process. Under both Ordinary Differential Equation (ODE) and Stochastic Differential Equation (SDE) sampling methods, DEFAR yields performance gains. Robustness to Inference Steps. Potential prediction bias can accumulate during inference. Increasing inference steps often amplifies exposure bias. To assess this effect, we evaluate all methods under various step settings. DEFAR consistently achieves the lowest FID across nearly all settings, maintaining stable performance as the sampling step increases in Tab. 4 (right).

7

Conclusion

This work introduces DEFAR, a framework designed to adaptively mitigate exposure bias by exploiting its intrinsic properties rather than relying on passive robustness. We demonstrate that exposure bias serves as a valuable signal, providing both directional guidance and frequency weighting cues. By integrating Anti-Drift Rectification (ADR) and Frequency Compensation (FC), DEFAR empowers the model to perform dynamic self-rectification based on its own deviations. Extensive experiments verify the superior performance, scalability, compatibility, and inference robustness of DEFAR across various benchmarks.

Acknowledgements The research of Shao-Lun Huang is supported in part by National Key R&D Program of China under Grant 2021YFA0715202, the National Natural Science Foundation of China under Grants 62571296 and Huawei.

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References 1. Adam, K.D.B.J., et al.: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 1412(6) (2014) 2. Albergo, M.S., Vanden-Eijnden, E.: Building normalizing flows with stochastic interpolants. In: The Eleventh International Conference on Learning Representations 3. Bai, C., Li, Y., Zhao, Z., Chen, J., Jia, P., She, Q., Lu, M., Zhang, S.: Fastinit: Fast noise initialization for temporally consistent video generation. arXiv preprint arXiv:2506.16119 (2025) 4. Bengio, S., Vinyals, O., Jaitly, N., Shazeer, N.: Scheduled sampling for sequence prediction with recurrent neural networks. Advances in neural information processing systems 28 (2015) 5. Chen, Z., Seetharaman, P., Russell, B., Nieto, O., Bourgin, D., Owens, A., Salamon, J.: Video-guided foley sound generation with multimodal controls. In: Proceedings of the Computer Vision and Pattern Recognition Conference. pp. 18770–18781 (2025) 6. Daras, G., Dagan, Y., Dimakis, A., Daskalakis, C.: Consistent diffusion models: Mitigating sampling drift by learning to be consistent. Advances in Neural Information Processing Systems 36, 42038–42063 (2023) 7. Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: Imagenet: A large-scale hierarchical image database. In: CVPR. pp. 248–255. Ieee (2009) 8. Deng, Y., Kojima, N., Rush, A.M.: Markup-to-image diffusion models with scheduled sampling. In: The Eleventh International Conference on Learning Representations 9. Dhariwal, P., Nichol, A.: Diffusion models beat gans on image synthesis. Advances in neural information processing systems 34, 8780–8794 (2021) 10. Ding, D., Ju, Z., Leng, Y., Liu, S., Liu, T., Shang, Z., Shen, K., Song, W., Tan, X., Tang, H., et al.: Kimi-audio technical report. arXiv preprint arXiv:2504.18425 (2025) 11. Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., et al.: An image is worth 16x16 words: Transformers for image recognition at scale. In: International Conference on Learning Representations 12. Everaert, M.N., Fitsios, A., Bocchio, M., Arpa, S., Süsstrunk, S., Achanta, R.: Exploiting the signal-leak bias in diffusion models. In: Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. pp. 4025–4034 (2024) 13. Fang, H., Qiu, D., Mao, B., Yan, P., Tang, H.: Motioncharacter: Identity-preserving and motion controllable human video generation. arXiv e-prints pp. arXiv–2411 (2024) 14. Frans, K., Hafner, D., Levine, S., Abbeel, P.: One step diffusion via shortcut models. In: International Conference on Learning Representations. vol. 2025, pp. 34668– 34684 (2025) 15. Geng, Z., Deng, M., Bai, X., Kolter, Z., He, K.: Mean flows for one-step generative modeling. Advances in Neural Information Processing Systems 38, 75460–75482 (2026) 16. Guo, Y., Wang, W., Yuan, Z., Cao, R., Chen, K., Chen, Z., Huo, Y., Zhang, Y., Wang, Y., Liu, S., et al.: Splitmeanflow: Interval splitting consistency in few-step generative modeling. arXiv preprint arXiv:2507.16884 (2025) 17. Haji-Ali, M., Menapace, W., Skorokhodov, I., Sahni, A., Tulyakov, S., Ordonez, V., Siarohin, A.: Improving progressive generation with decomposable flow matching. Advances in Neural Information Processing Systems 38, 163844–163885 (2026)

DEFAR for Exposure Bias Alleviation.

17

18. Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., Hochreiter, S.: Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems 30 (2017) 19. Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in neural information processing systems 33, 6840–6851 (2020) 20. Huang, F., Huang, G., Fan, X., He, Y., Liang, X., Chen, X., Jiang, Q., Khan, F.N., Jiang, J., Wang, Z.: Semantic-space exploration and exploitation in RLVR for LLM reasoning. In: Liakata, M., Moreira, V.P., Zhang, J., Jurgens, D. (eds.) Findings of the Association for Computational Linguistics: ACL 2026. pp. 38402– 38449. Association for Computational Linguistics, San Diego, California, United States (Jul 2026), https://aclanthology.org/2026.findings-acl.1915/ 21. Huang, F., Jiang, J., Jiang, Q., Li, H., Khan, F.N., Wang, Z.: Cosmic: Cliqueoriented semantic multi-space integration for robust clip test-time adaptation. In: Proceedings of the Computer Vision and Pattern Recognition Conference. pp. 9772–9781 (2025) 22. Huang, F., Yao, Z., Zhou, W.: Dtbs: Dual-teacher bi-directional self-training for domain adaptation in nighttime semantic segmentation. In: ECAI 2023, pp. 1084– 1091. IOS Press (2023) 23. Huang, X., Chen, Z., Shen, W., Zhang, X.P.: Learnibridge: Learnable calibration of feature caching for diffusion models acceleration. In: Forty-third International Conference on Machine Learning (2026), https://openreview.net/forum?id= 8sD74Krbw7 24. Kim, D., Kim, Y., Kwon, S.J., Kang, W., Moon, I.C.: Refining generative process with discriminator guidance in score-based diffusion models. In: International Conference on Machine Learning. pp. 16567–16598. PMLR (2023) 25. Kim, D., Lai, C.H., Liao, W., Murata, N., Takida, Y., Uesaka, T., He, Y., Mitsufuji, Y., Ermon, S.: Consistency trajectory models: Learning probability flow ode trajectory of diffusion. In: International Conference on Learning Representations. vol. 2024, pp. 44493–44525 (2024) 26. Kim, K., Kim, S.: Model already knows the best noise: Bayesian active noise selection via attention in video diffusion model. arXiv preprint arXiv:2505.17561 (2025) 27. Krizhevsky, A., et al.: Learning multiple layers of features from tiny images (2009) 28. Kulikov, V., Kleiner, M., Huberman-Spiegelglas, I., Michaeli, T.: Flowedit: Inversion-free text-based editing using pre-trained flow models. In: Proceedings of the IEEE/CVF International Conference on Computer Vision. pp. 19721–19730 (2025) 29. Kynkäänniemi, T., Karras, T., Laine, S., Lehtinen, J., Aila, T.: Improved precision and recall metric for assessing generative models. Advances in neural information processing systems 32 (2019) 30. Labs, B.F., Batifol, S., Blattmann, A., Boesel, F., Consul, S., Diagne, C., Dockhorn, T., English, J., English, Z., Esser, P., Kulal, S., Lacey, K., Levi, Y., Li, C., Lorenz, D., Müller, J., Podell, D., Rombach, R., Saini, H., Sauer, A., Smith, L.: Flux.1 kontext: Flow matching for in-context image generation and editing in latent space (2025), https://arxiv.org/abs/2506.15742 31. Li, M., Qu, T., Yao, R., Sun, W., Moens, M.F.: Alleviating exposure bias in diffusion models through sampling with shifted time steps. In: International Conference on Learning Representations. vol. 2024, pp. 16816–16838 (2024) 32. Li, Y., van der Schaar, M.: On error propagation of diffusion models. In: International Conference on Learning Representations. vol. 2024, pp. 32791–32807 (2024)

18

G. Huang, J. Mao, F. Huang et al.

33. Liang, Y., Cai, Z., Xu, J., Huang, G., Wang, Y., Liang, X., Liu, J., Li, Z., Wang, J., Huang, S.L.: Unleashing region understanding in intermediate layers for mllmbased referring expression generation. Advances in Neural Information Processing Systems 37, 120578–120601 (2024) 34. Lin, Z., Gao, Y., Yang, Y., Sang, J.: Revisiting visual model robustness: A frequency long-tailed distribution view. Advances in Neural Information Processing Systems 36, 59239–59251 (2023) 35. Lipman, Y., Chen, R.T., Ben-Hamu, H., Nickel, M., Le, M.: Flow matching for generative modeling. In: The Eleventh International Conference on Learning Representations 36. Liu, X., Gong, C., et al.: Flow straight and fast: Learning to generate and transfer data with rectified flow. In: The Eleventh International Conference on Learning Representations 37. Liu, Z., Luo, P., Wang, X., Tang, X.: Deep learning face attributes in the wild. In: Proceedings of the IEEE international conference on computer vision. pp. 3730– 3738 (2015) 38. Luo, X., Li, Q., Li, Y., Huang, G., Zhu, Y., Qin, W., Wang, M., Wan, P., Huang, S.L.: Beyond the golden data: Resolving the motion-vision quality dilemma via timestep selective training. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 43440–43449 (2026) 39. Luo, Y., Du, D., Huang, H., Fang, Y., Wang, M.: Curveflow: Curvature-guided flow matching for image generation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 9020–9029 (2026) 40. Ma, N., Goldstein, M., Albergo, M.S., Boffi, N.M., Vanden-Eijnden, E., Xie, S.: Sit: Exploring flow and diffusion-based generative models with scalable interpolant transformers. In: ECCV. pp. 23–40. Springer (2024) 41. Nash, C., Menick, J., Dieleman, S., Battaglia, P.: Generating images with sparse representations. In: International Conference on Machine Learning. pp. 7958–7968. PMLR (2021) 42. Ning, M., Li, M., Su, J., Salah, A.A., Onal Ertugrul, I.: Elucidating the exposure bias in diffusion models. In: International Conference on Learning Representations. vol. 2024, pp. 15167–15189 (2024) 43. Ning, M., Sangineto, E., Porrello, A., Calderara, S., Cucchiara, R.: Input perturbation reduces exposure bias in diffusion models. In: International Conference on Machine Learning. pp. 26245–26265. PMLR (2023) 44. Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al.: Pytorch: An imperative style, highperformance deep learning library. Advances in neural information processing systems 32 (2019) 45. Peebles, W., Xie, S.: Scalable diffusion models with transformers. In: ICCV. pp. 4195–4205 (2023) 46. Ranzato, M., Chopra, S., Auli, M., Zaremba, W.: Sequence level training with recurrent neural networks. arXiv preprint arXiv:1511.06732 (2015) 47. Ren, Z., Zhan, Y., Ding, L., Wang, G., Wang, C., Fan, Z., Tao, D.: Multi-step denoising scheduled sampling: Towards alleviating exposure bias for diffusion models. In: AAAI. vol. 38, pp. 4667–4675 (2024) 48. Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: CVPR. pp. 10684–10695 (2022) 49. Sabour, A., Fidler, S., Kreis, K.: Align your flow: Scaling continuous-time flow map distillation. Advances in Neural Information Processing Systems 38, 146459– 146512 (2026)

DEFAR for Exposure Bias Alleviation.

19

50. Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., Chen, X.: Improved techniques for training gans. Advances in neural information processing systems 29 (2016) 51. Schmidt, F.: Generalization in generation: A closer look at exposure bias. In: Proceedings of the 3rd Workshop on Neural Generation and Translation. vol. 19, pp. 157–167. Association for Computational Linguistics (2019) 52. Sigillo, L., He, S., Comminiello, D.: Latent wavelet diffusion: Enabling 4k image synthesis for free. arXiv e-prints pp. arXiv–2506 (2025) 53. Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., Ganguli, S.: Deep unsupervised learning using nonequilibrium thermodynamics. In: International conference on machine learning(ICML). pp. 2256–2265. pmlr (2015) 54. Song, Y., Dhariwal, P., Chen, M., Sutskever, I.: Consistency models. In: Proceedings of the 40th International Conference on Machine Learning. pp. 32211–32252 (2023) 55. Song, Y., Ermon, S.: Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems 32 (2019) 56. Tang, J., Li, J., Gao, Z., Li, J.: Rethinking graph neural networks for anomaly detection. In: International conference on machine learning. pp. 21076–21089. PMLR (2022) 57. Team, M.L., Cai, X., Huang, Q., Kang, Z., Li, H., Liang, S., Ma, L., Ren, S., Wei, X., Xie, R., et al.: Longcat-video technical report. arXiv preprint arXiv:2510.22200 (2025) 58. Tong, A., Fatras, K., Malkin, N., Huguet, G., Zhang, Y., Rector-Brooks, J., Wolf, G., Bengio, Y.: Improving and generalizing flow-based generative models with minibatch optimal transport. Transactions on Machine Learning Research pp. 1–34 (2024) 59. Venkatraman, A., Boots, B., Hebert, M., Bagnell, J.A.: Data as demonstrator with applications to system identification. In: ALR Workshop, NIPS (2014) 60. Wan, T., Wang, A., Ai, B., Wen, B., Mao, C., Xie, C.W., Chen, D., Yu, F., Zhao, H., Yang, J., et al.: Wan: Open and advanced large-scale video generative models. arXiv preprint arXiv:2503.20314 (2025) 61. Wang, C., Sennrich, R.: On exposure bias, hallucination and domain shift in neural machine translation. In: Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. pp. 3544–3552 (2020) 62. Wang, S., Azadi, S., Girdhar, R., Rambhatla, S., Sun, C., Yin, X.: Motif: Making text count in image animation with motion focal loss. In: Proceedings of the Computer Vision and Pattern Recognition Conference. pp. 7773–7783 (2025) 63. Wang, S., Tian, Z., Huang, W., Wang, L.: Ddt: Decoupled diffusion transformer. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 40633–40642 (2026) 64. Wu, T., Si, C., Jiang, Y., Huang, Z., Liu, Z.: Freeinit: Bridging initialization gap in video diffusion models. In: European conference on computer vision. pp. 378–394. Springer (2024) 65. Yao, Y., Chen, J., Huang, Z., Lin, H., Wang, M., Dai, G., Wang, J.: Manifold constraint reduces exposure bias in accelerated diffusion sampling. In: International Conference on Learning Representations. vol. 2025, pp. 96580–96616 (2025) 66. Yu, M., Zhan, K.: Frequency regulation for exposure bias mitigation in diffusion models. In: Proceedings of the 33rd ACM International Conference on Multimedia. pp. 10370–10378 (2025)

20

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67. Yu, S., Kwak, S., Jang, H., Jeong, J., Huang, J., Shin, J., Xie, S.: Representation alignment for generation: Training diffusion transformers is easier than you think. In: The Thirteenth International Conference on Learning Representations 68. Zhang, G., Shi, C., Jiang, Z., Xiang, X., Qian, J., Shi, S., Jiang, L.: Proteusid: Id-consistent and motion-coherent video customization. In: Proceedings of the SIGGRAPH Asia 2025 Conference Papers. pp. 1–11 (2025) 69. Zhang, J., Liu, D., Park, E., Zhang, S., Xu, C.: Anti-exposure bias in diffusion models. In: The Thirteenth International Conference on Learning Representations 70. Zhang, Q., Fu, H., Huang, G., Liang, Y., Chu, C., Peng, T., Wu, Y., Li, Q., Li, Y., Huang, S.L.: A high-dimensional statistical method for optimizing transfer quantities in multi-source transfer learning. Advances in Neural Information Processing Systems 38, 25528–25563 (2026) 71. Zhang, W., Feng, Y., Meng, F., You, D., Liu, Q.: Bridging the gap between training and inference for neural machine translation. In: Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. pp. 4334–4343 (2019) 72. Zhang, Y., Gu, J., Wu, Z., Zhai, S., Susskind, J., Jaitly, N.: Planner: Generating diversified paragraph via latent language diffusion model. Advances in Neural Information Processing Systems 36, 80178–80190 (2023) 73. Zhao, M., Zhu, H., Xiang, C., Zheng, K., Li, C., Zhu, J.: Identifying and solving conditional image leakage in image-to-video diffusion model. Advances in Neural Information Processing Systems 37, 30300–30326 (2024) 74. Zheng, J., Hu, M., Fan, Z., Wang, C., Ding, C., Tao, D., Cham, T.J.: Trajectory consistency distillation: Improved latent consistency distillation by semi-linear consistency function with trajectory mapping. arXiv preprint arXiv:2402.19159 (2024)

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21

Notations

Symbol Description x∗ Target data xt The forward linear interpolation between data and Gaussian noise at timestep t x̂t0 ,t1 The reverse predicted biased sample from timestep t0 to timestep t1 x̂∗ The final predicted biased endpoint ϵ Gaussian noise vt The predicted velocity from the model taking the forward perturbed xt as input vtarget The FM target velocity, typically x∗ − ϵ v̂t0 ,t1 The predicted velocity from the model taking the reverse-predicted biased input x̂t0 ,t1 as input vADR The reconstructed anti-drift rectification target V The frequency-domain representation of the velocity map vlow/high The low- / high-frequency components on velocity map after IFFT transforming MLFR/HFR The dominant low- / high-frequency mask of vtarget t The timestep and t ∈ [0, 1] t0/1 The starting / ending timestep of the single-step training-time inference process, with t1 > t0 θ Model parameters fθ (·) The velocity prediction function parameterized by θ p(·) The distribution function L The overall loss LADR The anti-drift rectification loss LFC The frequency compensation loss L The loss map with shape H × W L L̃ The normalized loss map of L N Normal distribution δ t0 ,t1 The exposure bias during time interval from t0 to t1 PFR The low-frequency components dominant ratio on velocity FEL The ratio in the loss that emphasizes the low-frequency components of vtarget DFT / FFT / IFFT Discrete Fourier Transform / Fast Fourier Transform / Inverse Fast Fourier Transform FLP/HP The low-pass / high-pass filter Wt0 ,t1 The frequency-aware weight modulated by exposure bias (u, v) The coordinates of the frequency-domain signal R The real part of DFT result I The imaginary part of DFT result D Training dataset H ×W The height and width shape of a sample α The coefficient modulating the influence of exposure bias on the frequency-aware weight ξ The stability constant β1 The hyperparameter of ADR loss β2 The hyperparameter of FC loss η Learning rate ϵ′ The predicted Gaussian noise a, b The interpolation coefficients

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Table 6: Directional normalization stabilizes training. Results are reported using a SiT-B/4 model trained for 250k iterations on the CIFAR-10 conditional generation task with 50 NFEs, without Classifier-Free Guidance (CFG). CIFAR-10 (cond) Method SiT DEFAR DEFAR DEFAR DEFAR (ours) DEFAR (ours)

B

Normalization

Direction

Iteration

/ / Rescale Unit Length Unit Length Unit Length

/ Anti-Drift Anti-Drift Directly Straight Anti-Drift Anti-Drift

250k 250k 250k 250k 120k 250k

FID↓

IS↑

14.09 317.31 20.20 12.15 12.01 11.22

8.22 1.38 7.93 8.25 8.27 8.31

Additional Ablation Studies

This section presents further ablation studies on components of our proposed method, along with details regarding the implementation hyperparameters. B.1

Effectiveness of Normalization for Anti-Drift Target

In this section, we further analyze why normalizing the anti-drift target is essential and provide empirical evidence to demonstrate its importance. Without normalization, the anti-drift target misguides the model toward noisy outputs. Removing both the flow-matching loss and the normalization, we force the model to directly predict the raw anti-drift target. Let t = 0 denote the pure noise distribution and t = 1 denote the data distribution. The generalized predicted velocity can be parameterized as: \label {eq:raw_target_merged} \mathbf {v}_\text {\ourdri {}} = a'_t\mathbf {x}_*+b'_t\hat {\mathbf {x}}_{t_0,t_1}.

(17)

While Eq. 17 formulates the target for a specific training interval from t0 to t1 , the actual inference process entails a continuous integration. During inference, at any continuous timestep t, the model takes the intermediate state x̂t as input, which has accumulated drift from previous steps. Assuming the model perfectly learns this unnormalized target mapping and applies it at each continuous step t, the endpoint of the inference trajectory starting from pure noise x0 = ϵ is derived as: \begin {aligned} \label {eq:unnormalization_result_general} \hat {\mathbf {x}}_* &= \pmb {\epsilon } + \int _0^1 (a'_t\mathbf {x}_* + b'_t\hat {\mathbf {x}}_t)\,dt \\ &= \pmb {\epsilon } + \left ( \int _0^1 a'_t\,dt \right ) \mathbf {x}_* + \int _0^1 b'_t\hat {\mathbf {x}}_t\,dt. \end {aligned} (18)

R1 In practice, the integral term 0 b′t x̂t dt cannot completely cancel the initial noise ϵ . This is because the intermediate state x̂t inherently deviates from the marginal distribution of the standard forward process due to the accumulated sampling drift. Consequently, the approximation error compounds along the denoising trajectory. Even with a perfectly learned target, the model lacks the capability to fully recover the ground truth sample x∗ , which explains the severe performance

DEFAR for Exposure Bias Alleviation.

23

degradation when directly learning Eq. 17, as reported in the second row of Tab. 6. Rescaling the anti-drift target introduces training instability. Directly learning the anti-drift target is problematic because the distribution of \protect \hat {\mathbf {x}}_{t_0,t_1} varies across different timestep intervals t_0,t_1 . A natural alternative is to rescale the anti-drift target so that its magnitude matches the standard flow matching objective (a'_t\mathbf {x}_* + b'_t \pmb {\epsilon }). Concretely, we divide the target by the effective time length: \label {eq:rescaled_target} \mathbf {v}_{\text {Rescaled \ourdri {}}} = \frac {a'_t\mathbf {x}_*+b'_t\hat {\mathbf {x}}_{t_0,t_1}}{1-t_1}.

(19)

This velocity alignment ensures that integrating the rescaled direction from 0 to 1 achieves the correct magnitude. However, during training, t_1 is sampled uniformly over the full interval [0,1]. As t_1 \to 1, the scaling factor 1/(1-t_1) in Eq. (19) diverges, leading to exploding losses and numerical instability. This inherent instability is directly reflected in the degraded generation results shown in the third row of Tab. 6. Normalization ensures stable directional guidance for anti-drift rectification. To avoid numerical instability while preserving crucial directional information, we explicitly normalize both the predicted velocity and the antidrift target to unit length. The final directional regularization term added to the flow-matching objective is defined as: \label {eq_appdix:adr_loss} \begin {aligned} \mathcal {L}_{\text {\ourdri {}}} &= \mathbb {E}_{\mathbf {x}_*, \hat {\mathbf {x}}_{t_0,t_1}, t_0,t_1} \left [ \left \| \frac {\mathbf {v}_{\theta }(\hat {\mathbf {x}}_{t_0,t_1}, t_1)}{\|\mathbf {v}_{\theta }(\hat {\mathbf {x}}_{t_0,t_1}, t_1)\|_2} - \frac {a'_{t_1} \mathbf {x}_* + b'_{t_1} \hat {\mathbf {x}}_{t_0,t_1}}{\|a'_{t_1} \mathbf {x}_* + b'_{t_1} \hat {\mathbf {x}}_{t_0,t_1}\|_2} \right \|^2 \right ]. \end {aligned}

(20)

This formulation preserves the standard flow-matching framework while explicitly guiding the predicted direction back to the true data distribution x∗ . Importantly, the inference velocity retains the correct magnitude scale inherited from the primary flow-matching loss term. As a result, integrating this velocity from 0 to 1 yields meaningful and highly stable generation, culminating in the best overall performance demonstrated in Tab. 6. Compatibility analysis: Anti-Drift vs. Direct State-Correction. We further investigate whether the model can simply learn a target direction that directly returns to the forward trajectory at timestep t1 . Specifically, we formulate a direct state-correction direction pointing from the drifted state to the forward perturbed state, (xt1 − x̂t0 ,t1 ), and apply unit-length normalization. The results are reported in the fourth row of Tab. 6 ("Directly Straight"). This experiment not only highlights the necessity of our specific ADR target but also reveals a fundamental flaw in naive correction: directly learning a pathreturning correction vector severely conflicts with the primary flow-matching objective. Our proposed Anti-Drift direction remains perfectly compatible. Under an ideal scenario where perfect prediction is achieved (i.e., x̂t0 ,t1 = xt1 ), the ADR target naturally degenerates back to the original flow-matching target a′t x∗ + b′tϵ . Conversely, under the same perfect conditions, the direct statecorrection target collapses to a zero vector 0. This zero-vector target directly

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Table 7: Effectiveness of exposure bias for frequency compensation. We compare different weighting strategies for frequency compensation, including low-pass, high-pass, original-image, original-noise, and exposure bias weights. Results are reported using a SiT-B/4 model trained for 250k iterations on the CIFAR-10 conditional generation task without Classifier-Free Guidance (CFG). CIFAR-10 (cond) Method

Weight Type Objective

DEFAR w/o FC + Low Pass Low Pass DEFAR w/o FC + High Pass High Pass DEFAR w/o FC + Original Image x∗ DEFAR w/o FC + Original Noise ϵ DEFAR (ours) Exposure Bias

on LF M on LF M on LF M on LF M on LF M

FID↓

IS↑

11.94 13.14 12.49 13.66 11.22

8.29 8.06 8.20 8.04 8.31

contradicts the flow-matching objective, causing severe gradient conflicts during training and ultimately leading to suboptimal performance. B.2

Effectiveness of Exposure Bias for Frequency Compensation

The analysis in Sec. 4.3 demonstrates that the frequency deficiency of the model varies significantly across timesteps: it lacks low-frequency components during high-noise timesteps, but accumulates excessive low-frequency content during low-noise timesteps. As shown in Tab. 7, methods that directly inject fixed lowor high-frequency components of the original image (Rows 1 and 2), or inject the original image or noise directly (Rows 3 and 4), only partially correct the deficiency while exacerbating the opposing frequency imbalance of the model. In contrast, our exposure bias formulation provides a dynamic signal that accurately reflects the instantaneous frequency shortfall of the model. It adaptively supplements low-frequency information when the model lacks it during high-noise timesteps, and naturally decreases this supplementation when lowfrequency components become dominant during low-noise timesteps. This adaptive behavior leads to the best overall performance, as demonstrated in Tab. 7. It is also worth noting that injecting exclusively low-frequency information consistently outperforms injecting exclusively high-frequency information (e.g., low-pass vs. high-pass, original image vs. original noise). This indicates that low-frequency learning has a more substantial impact on the final generative performance. Since exposure bias dynamically compensates for the specific lowfrequency content the model lacks, these results further highlight the effectiveness of exposure bias as a frequency-aware corrective signal. B.3

Hyperparameter Ablation of Our Methods

The results in Tab. 8 show that DEFAR remains robust under perturbed hyperparameters. On ImageNet-256, DEFAR improves over the SiT-B/4 baseline by 0.30–1.24 FID across the tested settings, while on CIFAR-10 it improves FID by 0.31–2.08. These results indicate that the gains are not restricted to a single carefully tuned configuration.

DEFAR for Exposure Bias Alleviation.

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Table 8: Hyperparameter robustness across datasets and backbones. Results are reported using 50 NFEs without Classifier-Free Guidance (CFG). Across perturbed hyperparameter settings, DEFAR consistently improves over SiT on ImageNet-256 and CIFAR-10. We include a SiT-M/2 setting with a deliberately suboptimal β2 . ImageNet-256 Method Backbone NFE β1 β2 α

Hour FID↓ ∆FID IS↑

CIFAR-10 ∆IS Hour FID↓ ∆FID IS↑

∆IS

SiT DEFAR DEFAR DEFAR DEFAR DEFAR DEFAR DEFAR

SiT-B/4 SiT-B/4 SiT-B/4 SiT-B/4 SiT-B/4 SiT-B/4 SiT-B/4 SiT-B/4

50 50 50 50 50 50 50 50

- - - 166 61.64 -0.00 24.67 +0.00 1 1.0 1.0 144 60.69 -0.95 25.85 +1.18 10 1.0 1.0 144 60.40 -1.24 26.21 +1.54 50 1.0 1.0 144 60.83 -0.81 25.71 +1.04 10 0.5 1.0 144 61.13 -0.51 25.23 +0.56 10 5.0 1.0 144 61.34 -0.30 24.91 +0.24 10 1.0 0.5 144 61.21 -0.43 25.09 +0.42 10 1.0 5.0 144 61.02 -0.62 25.44 +0.77

11 14.09 -0.00 8.22 +0.00 10 12.49 -1.60 8.26 +0.04 10 12.01 -2.08 8.27 +0.05 10 12.71 -1.38 8.26 +0.04 10 13.36 -0.73 8.24 +0.02 10 13.78 -0.31 8.21 -0.01 10 13.54 -0.55 8.23 +0.01 10 13.17 -0.92 8.25 +0.03

SiT DEFAR

SiT-M/2 SiT-M/2

50 50

- - - 311 30.57 -0.00 58.66 +0.00 10 5.0 1.0 330 30.11 -0.46 58.82 +0.16

-

-

-

-

-

The same trend also holds beyond the default backbone. Even with a deliberately suboptimal setting (β2 = 5.0), DEFAR improves the SiT-M/2 baseline by 0.46 FID on ImageNet-256. Therefore, we use β1 = 10, β2 = 1.0, and α = 1.0 as the default configuration in our main experiments, while the ablation confirms that moderate perturbations of these coefficients preserve consistent improvements. B.4

Multi-Step Scheduled Sampling Training for ADR

In our main experiments, we demonstrated that simulating a single inference step during training already yields substantial improvements. We further investigate whether extending this training procedure to multi-step inference provides additional gains. Recognizing that increasing the number of simulated inference steps inherently raises the computational cost, we specifically extend our baseline to two- and three-step variants for this ablation. Regarding the timestep selection, we evaluate two strategies. In the Random timestep sampling strategy, we first randomly sample an initial timestep t0 ∈ [0, 1], then sample the subsequent timestep t1 uniformly within (t0 , 1], and continue this process recursively for additional steps. In contrast, the Equal strategy first samples t0 , but then explicitly partitions the remaining sub-interval (t0 , 1] into n equal segments for an n-step simulation. Each subsequent timestep is then sampled randomly within its designated sub-interval. This mechanism enforces a more uniform temporal distribution, ensuring more stable timestep sampling compared to the fully random recursive scheme. As shown in Rows 2 and 3 of Tab. 9, two-step training can further improve generative performance over the one-step baseline (our main setting), provided a stable sampling strategy is used. However, extending the simulation to three steps leads to severe performance degradation (Rows 4 and 5). An explanation for this phenomenon is that excessively unrolling the simulated trajectories during training exacerbates the optimization difficulty. It compounds the variance of the

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Table 9: Effect of multi-step scheduled sampling for ADR. Results are reported for unconditional generation on CIFAR-10 with 50 NFEs. CIFAR-10 (uncond) Method

Steps Sampling Strategy Objective

DEFAR w/o FC DEFAR w/o FC DEFAR w/o FC DEFAR w/o FC DEFAR w/o FC

1 2 2 3 3

Random Random Equal Random Equal

FID↓

IS↑

Regularizer 15.92 Regularizer 21.89 Regularizer 15.33 Regularizer 148.95 Regularizer 32.20

7.83 8.10 8.04 3.76 7.30

Table 10: Effect of varying inference NFEs on ImageNet-256 with CFG. Results are reported using a SiT-B/4 model trained for 500k iterations on the conditional generation task. During training, the simulated trajectory is unrolled with 50 NFEs. SiT Steps 30 50 100 250 500

IP

SDSS

MDSS

Ours(250k) Ours(500k)

FID↓ IS↑ FID↓ IS↑ FID↓ IS↑ FID↓ IS↑ FID↓

IS↑

FID↓

32.62 55.64 30.30 59.14 31.48 58.24 33.05 56.61 30.36 31.64 55.65 29.84 60.20 30.29 58.69 31.90 56.89 29.81 31.14 55.51 28.76 59.04 29.66 58.66 31.20 56.93 28.69 30.96 55.15 28.76 58.59 29.42 58.38 30.93 56.63 28.56 30.94 54.98 28.55 58.32 29.41 58.14 30.90 56.57 28.41

56.31 58.81 59.01 58.95 58.81

29.36 56.43 28.34 58.94 28.05 59.39 27.95 59.38 27.87 59.36

IS↑

gradients backpropagated through the intermediate states, making it exceedingly difficult for the network to learn consistent transitions. Comparing the sampling strategies, the Equal strategy consistently outperforms the Random strategy, confirming its superior stability. B.5

Multi-NFE Generation on ImageNet-256 with CFG

In addition to evaluating multi-step sampling under the CFG-free setting, we further assess our method with a Classifier-Free Guidance (CFG) scale of 1.5 (following SiT [40]). As illustrated in Tab. 10, the observations remain highly consistent with the CFG-free scenario. With CFG enabled, our method maintains robust stability across diverse inference NFEs and consistently achieves the lowest FID scores. While the strong baseline IP obtains a competitive Inception Score (IS) at smaller NFEs, its performance noticeably degrades as the sampling steps increase (e.g., dropping from 60.20 at 50 NFEs to 58.32 at 500 NFEs). In contrast, our IS steadily improves and stabilizes at higher NFEs, ultimately surpassing all baselines.

C

More Related Work

Flow Rectification. Recent advances show that directly modifying flow trajectories can effectively enhance generation quality and stability. Several works aim to accelerate sampling by redesigning the flow operators. Shortcut Models [14] introduce shortcut paths to enable one-step generation, Mean Flows [15] approximate the expected flow for deterministic mapping, and SplitMeanFlow [16]

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Table 11: Configurations on ImageNet-256, CelebA-64 and CIFAR-10. Configs Dataset Params (M) Depth Hidden dim Heads Patch size Training iterations Global batch size Dropout Optimizer Lr schedule Learning rate Adam (βAdam,1 , βAdam,2 ) Weight decay Gradient clip Using NPUs α (exposure bias coeff.) β1 (ADR loss coeff.) β2 (FC loss coeff.)

SiT-B/4

SiT-M/2

SiT-XL/2

SiT-XL/2+ SiT-B/4 SiT-B/4

ImageNet-256 ImageNet-256 ImageNet-256 ImageNet-256 CelebA-64 CIFAR-10 131 308 675 675 131 131 12 16 28 28 12 12 768 1024 1152 1152 768 768 12 16 16 16 12 12 4×4 2×2 2×2 2×2 4×4 4×4 500k 256

500k 256

4

8

500k 256 0.0 Adam [1] constant 0.0001 (0.9, 0.999) 0.0 0.2 32

700k 256

250k 256

250k 128

32

4

1

1 10 1

enforces interval-wise consistency to stabilize few-step modeling. To reduce sampling drift, Consistency Models [54] and Consistent Diffusion [6] learn driftfree mappings via self-consistency, while Consistency Trajectory Models [25, 74] constrain entire probability flow ODE trajectories. In contrast, CurveFlow [39] leverages curvature to guide smoother flows, FlowEdit [28] modifies flow fields for text-based editing, and Align-Your-Flow [49] aligns student-teacher flow maps for scalable distillation. However, these methods primarily focus on acceleration, stability, or control, rather than explicitly addressing the exposure bias caused by the mismatch between training and inference in FM.

D

Additional Experimental Details

We follow the hyperparameters of Mean Flows [15] for ImageNet-256, and those of IP [43] for CIFAR-10 and CelebA-64, as detailed in Tab. 11. For ImageNet256, we utilize a standard VAE to compress images into 32 × 32 × 4 latent representations, which serve as the model inputs. We adopt SiT [40] as our primary backbone, which is built upon the ViT [11] architecture and employs adaLN-Zero [45] for class conditioning. We empirically observe that inheriting the default Classifier-Free Guidance (CFG) scales directly from the SiT baseline naturally yields the optimal generative performance for our method. For CIFAR10, the model operates directly on the 32 × 32 × 3 pixel space. We evaluate both conditional and unconditional generation on CIFAR-10. The conditional setup mirrors the ImageNet-256 configuration, while for the unconditional setting, we disable class conditioning by mapping all samples to a single default class. For

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CelebA-64, the model directly processes 64×64×3 pixel inputs for unconditional generation, similarly employing the single-class setup. Furthermore, to evaluate the scalability of our approach on high-resolution generation, we extend our experiments to ImageNet-512 using recent advanced architectures, REPA [67] and DDT [63]. To adapt them for higher resolution, we fine-tune their official pre-trained ImageNet-256 checkpoints on the ImageNet-512 dataset. For these advanced models, we adhere to their default configurations. Notably, consistent with our observations on SiT, we find that applying their respective default CFG scales also produces the best results for our method. All models are implemented in PyTorch 2.1 [44], optimized using the Adam [1] optimizer, and trained on Ascend 910B NPUs equipped with 64GB of memory. Regarding the statistical measurements, we carefully compute cumulative metrics, such as the Predicted Frequency Ratio (PFR) and the Frequency Emphasis of Loss (FEL). FEL depends on a temporal interval rather than a single isolated timestep. Specifically, to evaluate FEL at a target timestep t0 , we aggregate the exposure bias across all intermediate timesteps within the interval (t0 , 1]. This aggregated result is subsequently averaged across all evaluated samples. In all such statistical experiments, we discretize the continuous time domain [0, 1] into 50 uniform timesteps.

E

Baseline Implementation Details

SiT [40] Details. We directly follow the default hyperparameters and training configurations of the original SiT to train the backbone models and reproduce the baseline results. IP [43] Details. We adopt the default perturbation scale of 0.1. The core idea of IP is to add input perturbations to simulate inference-time errors. Following the original design, we inject an additional noise term of magnitude 0.1 into the intermediate states to mimic such inference errors and improve robustness to inference drift. This straightforward modification requires only a single-line code change to the original SiT implementation. SDSS [47] Details. The method highlights its most effective strategy to align predictions with the ground truth after simulating single inference step. This alignment improves passive robustness to drift accumulated during sampling. Following the paper, we implement SDSS within the SiT backbone under Flow Matching. At each iteration, we sample t0 < t1 in [0, 1] and infer one step from t0 to t1 . We then evaluate the velocity on the drifted state at t1 and align it with the target a′t x∗ + b′tϵ . MDSS [47] Details. The paper reports that four training-time inference steps offer the best trade-off, and we therefore adopt the same setup. We randomly sample two timesteps t0 , t1 ∈ [0, 1] with t0 < t1 , and perform single-step inference to reach the state at t1 . To simulate the extended four-step inference without incurring prohibitive computational overhead from recursive model forward passes, we directly accumulate the remaining three additional steps using

DEFAR for Exposure Bias Alleviation.

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the current trajectory formulation as an analytical approximation. Finally, we align the final prediction with the ground truth.

F

More Qualitative Comparison on ImageNet-256 and CelebA-64

In this section, we qualitatively compare DEFAR with several strong baselines (SiT, IP, SDSS, and MDSS). To ensure a strictly fair comparison, we use the exact same random seeds and initialize the sampling trajectories with identical starting noise across all models. As shown in Fig. 6 and Fig. 7, images generated by DEFAR consistently exhibit superior visual fidelity and structural coherence compared to those produced by the baselines. In Fig. 6, baseline models frequently fail to render key semantic structures accurately. For instance, they struggle with the bird’s feet and beak, the background trees, and the fine shading on the mushroom, often leading to overexposed patches or incomplete details. In stark contrast, DEFAR generates sharper boundaries, more coherent textures, and more faithfully reconstructed object parts. Similarly, in Fig. 7, the baseline models struggle to produce clean facial regions, leaving dark patches on the forehead, blurred or inconsistent hair structures, and incorrect semantic separation between the neck and clothing. They also exhibit severe artifacts around the facial contours and fail to maintain consistent geometry between the head and neck. Across all rows, DEFAR produces significantly cleaner facial details, more accurate hair topology, clearer backgroundto-foreground transitions, and drastically reduced color artifacts, culminating in a higher overall visual quality.

G

Generated Samples on ImageNet-256 with 50 NFEs

In this section, we present the images sampled by DEFAR to qualitatively evaluate the generative capability of our model, as shown in Fig. 8. We deploy our best-performing DEFAR-XL/2+ model and perform sampling with 50 NFEs and a CFG scale of 4.0 on the ImageNet-256 dataset. Across both landscapes and animal categories, the model produces exceptionally high-quality samples with fine-grained details. In many cases, DEFAR synthesizes realistic animal characteristics, including intricate fur textures, accurate eye reflections, and subtle motion cues. It also captures structurally complex and challenging landscapes, such as volcanic eruptions, with rich structural and textural fidelity.

H

More Frequency-Aware Visualization on ImageNet-256

In this section, we provide detailed visual examples illustrating that exposure bias inherently acts as a frequency-aware signal, specifically attending to lowfrequency regions in the original data. We employ a SiT-B/4 model trained for

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500k iterations and compute the exposure bias under high-noise timesteps for various samples. We then directly visualize the resulting exposure bias spatial maps, as shown in Fig. 9. The leftmost column of Fig. 9 displays the original ground-truth images. Applying standard high-pass and low-pass filters to these images yields their respective high-frequency and low-frequency components (second and third columns). The rightmost column presents the visualization of the raw exposure bias maps. Across the samples, the exposure bias consistently highlights core low-frequency regions, including dark clothing, sofas and nearby objects, sky regions in outdoor scenes, and the smooth surface of the phone casing. These results provide visual validation that exposure bias inherently attends to semantically meaningful low-frequency pixels during high-noise timesteps, dynamically guiding the network to compensate for low-frequency deficiencies.

DEFAR for Exposure Bias Alleviation.

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Ours

Fig. 6: Qualitative comparison across methods on ImageNet-256. All images are generated with 50 NFEs and a CFG scale of 1.5. Compared to the baseline methods, our approach (DEFAR) consistently yields superior visual fidelity, demonstrating more accurate semantic structures (e.g., the bird’s beak in Row 1, the background trees and architecture in Row 3) and fewer visual artifacts.

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IP

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Fig. 7: Qualitative comparison across methods on CelebA-64. All images are unconditionally generated with 50 NFEs. Compared to the baseline methods, our approach (DEFAR) consistently yields superior visual fidelity, demonstrating cleaner facial details, more coherent hair structures, and significantly fewer artifacts (e.g., notice the forehead patches in Row 1 and the distorted facial contours in Row 5).

DEFAR for Exposure Bias Alleviation.

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Fig. 8: Qualitative results on ImageNet-256. The samples are generated by our DEFAR-XL/2+ model with 50 NFEs and a CFG scale of 4.0. The results demonstrate the model’s exceptional capability to synthesize structurally complex scenes and fine-grained details (e.g., intricate animal fur and natural reflections) with high visual fidelity.

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Raw Images

High Pass

Low Pass

Awared Low-Freq.

Fig. 9: Exposure bias highlights low-frequency structures in images. We analyze the frequency components of raw images as references and observe that exposure bias consistently aligns with low-pass regions. These examples are from ImageNet-256.