Rethinking the design space of Vanilla Pixel Diffusion Transformers

R ETHINKING THE DESIGN SPACE OF VANILLA P IXEL D IFFUSION T RANSFORMERS Soumik Mukhopadhyay1,2∗ Long Mai2 Abhinav Shrivastava1 University of Maryland, College Park 2 Adobe Research

Aniruddha Mahapatra2†

arXiv:2610.23854v1 [cs.CV] 16 Oct 2026

1

Figure 1: Sample 512px text-to-image generations with our MF LOW-XXL/16 model.

A BSTRACT Pixel-space diffusion models have recently re-emerged as a compelling alternative to latent diffusion, avoiding the lossy latent bottleneck and separately trained autoencoder. JiT shows that a vanilla diffusion transformer can generate directly in pixel space by replacing the commonly used velocity prediction (u) with clean image prediction (x0 ). In this work, we revisit this choice and introduce MF LOW, an adaptive parameterization that learns to interpolate between x0 and u prediction across principal directions of the data, which can be learned end-to-end with diffusion model training. We find that the preferred parameterization varies systematically with the data representation and model capacity. Notably, increasing model capacity shifts preference toward u prediction from x0 prediction. We evaluate MF LOW across ImageNet, UCF-101 video, and large-scale text-to-image generation, demonstrating competitive or improved generative performance across diverse settings. In addition, we find that vanilla pixel diffusion transformers, irrespective of parameterization, retain a persistent high-frequency deficit relative to real images. To address this, we introduce ConvRefiner, a lightweight convolutional module trained post-hoc with adversarial loss while keeping the diffusion backbone frozen. With only a small amount of additional training, ConvRefiner restores the high-frequency statistics of generated images while preserving FID. Project webpage: soumik-kanad.github.io/mflow-diffusion.

1

I NTRODUCTION

Diffusion and flow-based models have become a leading paradigm for visual generation in recent years. Modern versions of these models predominantly operate in the latent space, obtained from compressing the pixel-space data with a separately-trained autoencoder. However, latent diffusion ∗ †

Work done while an intern at Adobe Research. Project lead.

1

models (LDMs) (Rombach et al. (2022); Peebles & Xie (2023); Ma et al. (2024); Esser et al. (2024); Yu et al. (2025); Singh et al. (2026)) introduce their own limitations – a lossy bottleneck leads to unfaithful reconstruction after compression, and there is a need for a separately trained compression autoencoder, which is typically unaware of the downstream generative objective. Recent works (Li & He (2026); Chen et al. (2026b); Yu et al. (2026); Mukhopadhyay et al. (2026); Chen et al. (2025b); Ma et al. (2026b;c); Wang et al. (2026c)) have revived diffusion directly in pixel space for image generation, removing the aforementioned drawbacks in LDMs. In particular, JiT (Li & He (2026)), demonstrates that vanilla diffusion transformers can achieve competitive generative performance directly on raw pixels, eliminating the need for pretrained autoencoders or complicated architectural modifications. Its aggressive patchification keeps the sequence length manageable, e.g., its 16 × 16 patchification produces equivalent number of tokens as a 16× spatial compression VAE followed by 1 × 1 latent patchification. At the same time, such aggressive patchification poses a challenge in pixel-space diffusion as each token must model a high-dimensional block of raw pixels, raising two questions: what prediction parameterization is best suited to such high-dimensional patches, and can a vanilla large-patch transformer faithfully model fine-scale image details? In this work, we aim to improve the pixel-space diffusion paradigm along these axes. JiT addresses the first question with clean-image (x0 ) prediction. Under the manifold assumption, clean data lies near a low-dimensional manifold, whereas noise and velocity span the ambient space, making x0 easier for an undercomplete network to predict. However, sampling requires converting x0 to u (velocity), which becomes ill-conditioned near the low-noise regime. AsymFlow (Chen et al. (2026a)) reduces this problem by predicting u in a selected rank-r PCA subspace and x0 in its complement, keeping the prediction target effectively in a low dimensionality. However, this hard binary cutoff rank must be chosen for each setting through expensive training sweeps, e.g., AsymFlow needed 6 trainings to tune the rank-r. Where as Jin & Wang (2026) use a learnable but globally shared interpolation between x0 and u, not reducing the effective noise dimensionality. We introduce MF LOW, an adaptive parameterization with a continuous gain mi ∈ [0, 1] for every principal direction of data. Notably, this differentiable velocity-recovery formulation lets us jointly train the generator and gains with the standard velocity-space flow-matching loss, letting model learn the best combination of u and x0 per principal component. MF LOW therefore replaces the AsymFlow’s manually selected rank and binary mask with a continuous parameterization that adapts to the data representation, objective, and model capacity. Our experiments show that MF LOW can be adapted not only to pixel-space image generation, but also to diverse paradigms, like pixel-space video generation, text-to-image generation at multiple model capacities, and high-dimensional latents like RAEv2 (Singh et al. (2026)). Further visualization of the learned direction-wise gains as M -curves, a plot of mi ’s in decreasing direction variance order, reveal interesting insights, such as increasing model capacity shifts more directions toward velocity-like prediction. Prediction parameterization alone does not resolve all limitations of vanilla pixel diffusion transformers. Irrespective of the parameterization, we find that JiT-family models exhibit a persistent high-frequency deficit relative to real images. This suggests a limitation of the minimalist largepatch design, where patch tokens are projected directly back to pixels using MLP-layers without an explicit local refinement pathway. We introduce ConvRefiner, a lightweight residual convolutional module trained post hoc with perceptual and adversarial supervision while keeping the diffusion backbone frozen. With only 5% post-hoc training, ConvRefiner brings the generated high-frequency spectrum closer to that of real images while preserving FID. Overall, this work presents adaptive prediction parameterization and fine-scale signal modeling as complementary directions for improving vanilla pixel diffusion transformers. To summarize, the key contributions are: • We introduce MF LOW, a framework of continuous, direction-adaptive prediction parameterization whose gains are learned jointly with the generator under a standard velocity-space flowmatching objective. We show MF LOW is a general framework and can be used for diverse domains like pixel-space video generation, high-dimensional latents (like RAEv2) in addition to pixel-space image generation. • We identify a high-frequency deficit in vanilla JiT-style models and introduce ConvRefiner, a lightweight post-hoc module that restores high-frequency details while preserving fidelity matching the frequency spectrum of real images.

2

Figure 2: Additional Text-to-Image Results. Sample 512px text-to-image generations with our MFLOW-XXL/16 model.

3

2

R ELATED W ORK

Pixel-space diffusion and prediction parameterization. Early diffusion models generated directly in pixel space (Ho et al. (2020); Nichol & Dhariwal (2021); Dhariwal & Nichol (2021); Karras et al. (2022)), while subsequent works improved the scalability of end-to-end pixel generation through architectural and formulation advances (Jabri et al. (2023); Hoogeboom et al. (2023; 2025); Crowson et al. (2024); Chen et al. (2025b); Mukhopadhyay et al. (2026)). Recent approaches have renewed interest in pixel-space generation using vanilla or specialized transformer architectures (Li & He (2026); Chen et al. (2026b); Yu et al. (2026); Guo et al. (2026)), with recent studies further exploring its scaling to text-to-image generation (Jiang et al. (2026); Wang et al. (2026c); Ma et al. (2026b); Yu et al. (2026); Ma et al. (2026c); Chen et al. (2025b)). In the context of our parameterization study, JiT (Li & He (2026)) advocates clean-image prediction for high-dimensional pixel modeling, an approach also adopted by recent large-scale pixel-space models such as Tuna-2 (Liu et al. (2026)). k-Diff Jin & Wang (2026) and AsymFlow Chen et al. (2026a) further explore adaptive combinations of clean-data and velocity prediction. Instead of deciding a predefined fixed formulation, which can vary across architectures and datasets, MF LOW lets the model learn the best fit between clean image and velocity prediction. Details and frequency modeling. Several recent works study the difficulty of modeling fine-scale information in vanilla pixel-space diffusion transformers with large spatial patch sizes, such as 16 × 16–32 × 32. Existing approaches use perceptual supervision (Ma et al. (2026c)), frequencyaware objectives or flows (Degeorge et al. (2026); Pavasovic et al. (2026); Fan et al. (2026)), frequency-specialized architectures (Ma et al. (2026b;a)), or improved information pathways (Guo et al. (2026)). Concurrent work also shows that a frozen JiT model can recover additional highfrequency detail through self-guidance (Fu et al. (2026)). Although some of these approaches also improve training efficiency (Degeorge et al. (2026); Ma et al. (2026b)), they generally introduce specialized architectural components or modify the training objective, and their generated frequency statistics can still exhibit a high-frequency gap relative to real images (Degeorge et al. (2026); Ma et al. (2026b); Pavasovic et al. (2026)). In contrast, our lightweight ConvRefiner is trained post hoc while keeping the pretrained diffusion backbone frozen. It recovers the missing high-frequency statistics without modifying the backbone or its original training procedure, while preserving FID.

3

M ODEL P REDICTION PARAMETERIZATION

3.1

M OTIVATION

Flow Matching. In the linear stochastic interpolant/rectified-flow formulation used by SiT (Ma et al. (2024)) and JiT (Li & He (2026)), for signal x0 ∼ pdata and noise ϵ ∼ N (0, I), both in RD , the forward interpolation at timestep t: xt = t x0 +(1−t) ϵ. The generative process is the probabilityflow ODE that transports pure noise ϵ (t = 0) to clean signal x0 (t = 1) along  the conditional expect tation of the interpolant’s time derivative, the velocity field u(xt , t) = E dx dt xt = E[x0 − ϵ|xt ]. A network fθ (xt , t) is trained by regressing a target derived from (x0 , ϵ, t). Adaptive parameterization. Common non-adaptive parameterization/regression-targets include: noise ϵ-prediction, velocity u-prediction , and clean signal x0 -prediction. These are algebraically equivalent but differ in conditioning. EDM (Karras et al. (2022)) introduces an input/output preconditioning, where the network effectively predicts a noise-level dependent combination of clean data and noise. However, JiT (Li & He (2026)) demonstrates that such a preconditioning substantially underperforms x0 -prediction for high-dimensional pixel patches using a vanilla transformer backbone, motivating the use of standard clean image prediction. More recently, k-Diff (Jin & Wang (2026)) introduces a learnable scalar interpolation between prediction targets, showing that the preferred parameterization varies across pixel and latent representations. However, its globally shared coefficient cannot account for directional differences within a representation. AsymFlow (Chen et al. (2026a)) addresses this limitation by assigning velocity u-prediction to a selected low-rank subspace while clean image x0 -prediction in its complement. More concretely, let U = [v1 , . . . , vD ] be the orthonormal patch-PCA eigenvectors of the data (variances λ1 ≥ · · · ≥ λD ), and let A = U:,1:r be the top-r directions with AT A = Ir , then the orthogonal projector P = AAT has the properties P 2 = P and (I − P )P = 0. Their model predicts the asymmetric 4

JiT / x0-pred (mi = 0 )

Velocity u-pred (mi = 1 )

x0

-

mi 0

= x

0

x0

-

x0

mi 1

= u

Velocity / u -pred

JiT / x0-pred AsymFlow MFlow (top-K, mi ∈ {0,1}) (learnable, mi ∈ [0,1])

-

mi P

= u

A

x0

-

= u

G

MFlow

AsymFlow black = x0-pred

mi M

white = u-pred

Figure 3: Overview of MF LOW Formulation. We propose a principal data direction-wise learnable parameterization as a generalized framework in contrast with previous fixed parameterizations. target uA = x0 − P ϵ, i.e., predict the full clean signal, but only the low-rank projection of the noise. Because P is a projector, the target splits cleanly into the velocity inside the subspace P uA = P (x0 − ϵ) = P u, and the clean data on the complement (I − P ) uA = (I − P )x0 . So each PCA direction is treated either as velocity (i ≤ r) or as x0 (i > r). The full velocity is +uA recovered from uA and xt by: u = P uA + (I − P ) xt1−t . Limitations of previous adaptive parameterizations. Chen et al. (2026a) note that the default x0 -prediction and k-Diff parameterization are less expressive. On the other hand, AsymFlow makes hard-cutoff decision at a fixed rank r, and this chosen subspace is dataset/modality dependent, requiring an expensive hyperparameter search over multiple parameterization setting. Furthermore, restricting the noise term to the top-r (highest-variance) directions is arbitrary – e.g., we found that PCA[9 : 16] can beat PCA[1 : 8] (FID 3.54 vs 3.59 on the B-level model trained on ImageNet). Finally, the binary nature of the cutoff, while useful for interpretation, is not necessary: it extends naturally to a continuous, per-direction weighting that softly mixes the clean-signal (x0 ) and velocity (v) prediction. Building on these insights, we introduce MF LOW, which learns a continuous, direction-dependent parameterization, allowing the prediction target to adapt across directions without requiring a hard subspace partition or costly search for parameterization. 3.2

MF LOW : D IRECTION -A DAPTIVE L EARNABLE R EPARAMETERIZATION

Instead of a hard cutoff, we assign each spectral direction a soft, learnable weight in [0, 1]. Replace the binary projector P by a symmetric graded operator: M = U diag(m1 , . . . , mD ) U T ,

mi ∈ [0, 1],

M vi = mi vi ,

(1)

with the graded target (as shown in Fig. 3): uG = x0 − M ϵ . 2

(2) D

M is generally not a projector (M ̸= M unless every mi ∈ {0, 1}), so it does not split R into the low-rank subspace Im(P ) and its orthogonal complement Im(I − P ). Instead every direction carries its own continuous velocity-data mixing weight. Component-wise (PCA basis). Let x̃ := U T x denote the transformation of x in the PCA basis, gx)i = mi x̃i , then we have the ith component x̃i = viT x. Because M is diagonal in this basis, (M and the graded target decouples per direction: ũG,i = x̃0,i − mi ϵ̃i (3) where the directional velocity is ũi = x̃0,i − ϵ̃i . Here mi denotes how velocity-like the target is in this direction: mi = 1 ⇒ u-pred while mi = 0 ⇒ x0 -pred. MF LOW therefore strictly generalizes both the endpoints as well as AsymFlow (mi = 1[i ≤ r]). 5

i Choosing the gains. We initialize the gains with mi = λ̂λ̂+c where λ̂i = λi /λmax is the normalized i variance, and c is a small constant. By default these gains are learnable mi = sigmoid(ϕi ) with a learnable per-direction logit ϕi .

Exact velocity recovery. The forward xt = t x0 + (1 − t) ϵ and target Eq. (3) give two linear equations in the two unknowns(x̃0,i , ϵ̃i ) in each eigendirection:      x̃t,i t 1 − t x̃0,i = , (4) ũG,i 1 −mi ϵ̃i The system matrix has determinant −∆i with ∆i = (1 − t) + mi t ≥ 1 − t > 0; since it is nonzero (strictly negative) for every mi ∈ [0, 1] , the solve is always exact: x̃0,i =

(1 − t) ũG,i + mi x̃t,i , ∆i

ϵ̃i =

x̃t,i − t ũG,i , ∆i

Equivalently, in the operator form the vx0 and vu can be recovered from the target uG using:  −1   x0 = t M + (1 − t) I (1 − t) uG + M xt ,  −1   x0 − xt = t M + (1 − t) I uG − (I − M ) xt . u = 1−t

(5)

(6)

Setting mi ∈ {0, 1} reduces Eq (6) exactly to the AsymFlow recovery rule. Training and sampling. M changes neither the forward process nor the transport target u, only the coordinate-wise conditioning of the network’s regression target. The network outputs ûG as the learned approximation for target uG which we map it to the full velocity û via Eq (6) and train a velocity-space flow-matching loss,   L(θ) = Ex0 ,ϵ,t w(t) ∥û(ûG ; xt , t) − (x0 − ϵ)∥22 . (7) Additionally, we can add an LPIPS loss on the predicted clean signal when required. At sampling time we run standard Euler/Heun on ẋ = u with u from Eq. (6). 3.3

T OY E XAMPLE

We revisit the toy manifold experiment of JiT (Li & He (2026)) to test two properties of MF LOW: (a) whether continuous, non-binary m-values remain tractable in high-dimensional observation spaces, and (b) whether they can be learned jointly with the generator. We sample a 2D spiral and embed it into a D-dimensional space using a fixed random column-orthogonal projection. We fix the intrinsic dimension to d = 2, vary D ∈ {2, 8, 16, 512}, and train a five-layer ReLU MLP with 256 hidden units. We compare x0 prediction, full u-prediction, AsymFlow with r = d, MF LOW with fixed normalized-variance gains, and MF LOW with gains learned from the Figure 4: Toy manifold experiment. A 2-D same initialization. All variants use the same ar- spiral is embedded in D ∈ {2, 8, 16, 512} dichitecture and velocity-space training objective. mensions and projected back for visualization. As shown in Fig. 4, full u-prediction deterio- Full u-prediction degrades with D, while x 0 rates as D increases, whereas x0 -prediction and prediction, rank-matched AsymFlow, and fixed rank-matched AsymFlow remain stable. Both or learned MF LOW recover the spiral, including fixed and learnable MF LOW also recover the in the undercomplete D = 512 setting. spiral, including at D = 512. Thus, highdimensional tractability does not require binary gains mi ∈ {0, 1}: continuous gains remain effective. The learnable variant further shows that this allocation can be optimized end-to-end rather than specified in a heuristic manner. 6

4

S IGNAL M ODELING

4.1

M OTIVATION

JiT lacks high-frequency but some other pixel diffusion models do not. JiT’s minimalist architecture lacks an explicit pathway dedicated to fine-grained signal details, like skip connections (Bao et al. (2023); Hoogeboom et al. (2023; 2025)) or parallel refinement networks (Chen et al. (2026b); Yu et al. (2026)), motivating an investigation into whether this simplicity introduces limitations in its generated frequency distribution. We study the frequency spectrum of the images generated by models we trained which share the JiT architecture. We use radially averaged power spectrum (RAPS) for this analysis. For context, images on a pixel grid can have at most 0.5 cycles/pixel horizontal or vertical frequencies (fx ,fy ). However, in the case √ of radial averaging, the radial frequencies fr can reach till the diagonal frequency of 0.707 (= 0.52 + 0.52 ). Interestingly, as seen in Fig. 5, we observe that all these models lack radial frequencies in the range of 0.5 − 0.7. Recent concurrent works (Pavasovic et al. (2026); Degeorge et al. (2026); Fu et al. (2026)) have also observed this. As seen in Fig. 6, we tried investigating other LDMs and pixel diffusion backbones. We find that neither VAE-reconstruction/generations of DiT (Peebles & Xie (2023)), REPA-E (Leng et al. (2025)), nor the generations of PixelDiT (Yu et al. (2026)) (which as a pixel level pathway) suffer from this issue, indicating that it might be a JiT backbone specific problem, more explicitely the use of high patchidication (and unpatchification) of 16 − 32× without any intra-patch local operation.

Figure 5: JiT-family generations lacks high frequency irrespective of parameterization.

Figure 7: Overview of ConvRefiner Formulation. We propose a residual convolutional refiner post hoc Figure 6: Latent model generations, VAE re- training for a few epochs, with a fixed backbone, constructions, and other pixel diffusion mod- to regain the high-frequency similar to real images els like PixelDiT do not lack high frequency. spectrum in vanilla vision transformers.

4.2

C ONV R EFINER : A SIMPLE POST- HOC FIX

Based on our analysis we suspect that this high-frequency deficit might be specific to the JiT-based pixel diffusion architecture. However, as seen in the previous section, convolutional VAE decoders are able to recover highfrequency. Chen et al. (2025a) note that only finetuning the last few layers of a pretrained VAE with an adversarial loss can improve local details at a reduced training cost.

Table 1: Summary of Results. Our MF LOW + ConvRefiner provides a flexible parameterization, saving expensive hyperparameter sweeps while having better FID, as well as solving the highfrequency deficit (measured in mean radial power deficit compared to real images) on ImageNet-1K 256×256.

Motivated by this, we add a few lightweight convolutional blocks and post-hoc train only these blocks using Method FID↓ HF-deficit(dB) an additional GAN loss apart from flow-matchting losses JiT-H/16 1.82 -6.69 MF LOW-H/16 MF LOW 1.81 -6.63 (Fig 7). We keep the JiT backbone frozen to keep the reMF LOW-H/16 + ConvRefiner (ours) 1.81 -1.29 finement light. The ConvRefiner predicts a residual over x-prediction of the network on which the perceptual and adversarial losses are then applied. For other parameterizations, the prediction is first converted to x (clean image) and then the ConvRefiner residual is applied on top of it. 7

5

E XPERIMENTS

We extensively evaluate our proposed method on class-conditional ImageNet image generation to validate its effectiveness, as summarized in Table 1. Then we delve into individual components – MF LOW and ConvRefiner. We further show that MF LOW can be extended to video generation and scaled to text-to-image generation. Finally, we ablate the design decision of each component. Datasets and Evaluation. For class-conditioned image generation experiments we train on ImageNet-1K (Russakovsky et al. (2015)). By default we show results on the standard 256 × 256 resolution images with the training and evaluation similar to Li & He (2026). For evaluation we use FID@50K (Heusel et al. (2017)). We conduct class-conditioned video generation experiments on UCF-101 (Soomro et al. (2012)) dataset. We use 16 frames of 128 × 128 resolution videos for training and evaluation following Wang et al. (2025). Similar to images, FVD@10K (Unterthiner et al. (2018)) serves as our video generation evaluation metric. For text-to-image generation, we train on internal dataset of around 900M images (pretraining) and 33.5M (SFT), and evaluate on standard benchmarks of GenEval (Ghosh et al. (2023)), DPG-Bench (Hu et al. (2024)), and PRISM-Bench (Fang et al. (2026)). Implementation Details. We build on top of the JiT Table 2: Effect of LPIPS on Imarepository and use their architecture for conditional im- geNet 256×256 generation. We see age and video generation experiments. Hence, we use that LPIPS helps all the models in FID JiT both to refer to the vanilla transformer backbone and (evaluated on base JiT-B evaluation hyx0 -prediction parameterization (especially when compar- perparameters). However, it improves ing against MF LOW parameterization). We refer the base, MF LOW performance the most, beating large, and huge sizes as B-/L-/H-level. For these experi- the baselines. ments, for ImageNet we used patch size of 16×16 leading to 256 tokens (with additional 32 in-context tokens like FID↓ Method w/o LPIPS w/ LPIPS JiT), while for video we use 4 × 8 × 8 patch size (with JiT-B/16 (Li & He (2026)) 3.70 3.42 4 as the temporal patch size) leading to 1024 tokens. For AsymFlow-B/16 (Chen et al. (2026a)) 3.59 3.40 text-to-image, we train with a patch size of 16 × 16 on MF LOW-B/16 (ours) 3.74 3.33 mixed-resolution 256p and 512p images with LPIPS loss (0.1 loss weighting). For calculating patch-wise PCAbasis we follow AsymFlow. In the case of ConvRefiner, we use a PatchGAN (Isola et al. (2017)) to apply the GAN loss only on the near-clean images (see appendix for details). ImageNet. (a) MF LOW: On class-conditioned image generation on ImageNet 256×256 experiment at B-level, as shown in Table 2, without LPIPS loss and at the base JiT-B parameters, we observe that AsymFlow works better than both JiT and MF LOW. Based on PixelGen (Ma et al. (2026c)) we tried to add LPIPS loss to our baselines and MF LOW model, and found that it provides performance gain across the board. Surprisingly, we see that this addition makes MF LOW the best at this configuration. Subsequently, we train the same models with LPIPS at H-scale as shown in Table 3. We hypothesize the very slight lead of AsymFlow as a result of it being heavily tuned for ImageNet. Even so, we find that MF LOW is very competitive to all the prior pixel diffusion transformer models without any parameterization search. (b) ConvRefiner: We experiment with training the JiT and MF LOW models on ImageNet 256 × 256 using our ConvRefiner for an additional 30 epochs on top of the frozen 600 epoch trained base model. As shown in Fig. 8 (left), at both B- and H-levels and across both JiT and MF LOW we see that the high radial frequency deficit is fixed. At the same time, Fig. 8 (right) shows that this training maintains the FID. Hence, ConvRefiner is effective at solving the high-frequency problem without affecting the FID at all. We provide some visual improvement results in Fig. 22. Videos. We show the effectiveness of MF LOW in the domain of videos apart from images. At the B-level class-conditioned UCF-101 video generation as shown in Table 4, we see that MF LOW outperforms the WAN2.1 (Team (2025)) latent diffusion model, pixel-based JiT, and AsymFlow models we trained. We expand to L-level, where MF LOW beats JiT and AsymFlow. With a small post-hoc Framewise-LPIPS training, we achieve best performance. Notably, we find training with Framewise-LPIPS from start (like ImageNet) hurts video generation. Text-to-Image. (a) MF LOW: We study whether MF LOW scales beyond class-conditioned generation to large-scale text-to-image (T2I). We instantiate JiT, AsymFlow (r = 8), and MF LOW using the same 1.1B-parameter MMDiT-L/16 backbone and compare them under the same SFT setting. This controlled comparison isolates the effect of prediction parameterization while keeping the backbone and reported model size fixed. As shown in Table 6, the three parameterizations perform similarly 8

Table 3: ImageNet 256×256 comparisons. We trained JiT, AsymFlow, and MF LOW from scratch with additional LPIPS (Zhang et al. (2018)) loss (but without REPA (Yu et al. (2025))) and evaluated under the JiT protocol with individual hyperparameter tuning (denoted by *). We use the best hyperparameter for each after doing a sweep. The AsymFlow number remains in the range of the non-REPA performance noted in Chen et al. (2026a). We use AsymFlow’s FLOP convention as reported in Yu et al. (2026). Method

Table 4: UCF-101 video comparisons (Blevel). We show results on models we trained with best-tuned hyperparameters for each. Method WAN-VAE2.1-1.3B(4×8×8) + latent-DiT-B/1×1×1 Video JiT-B/4×8×8 (Li & He (2026)) Video AsymFlow-B/4×8×8 (Li & He (2026)) Video MF LOW-B/4×8×8 (ours)

554M

2240

4.59

Hierarchical transformers (skip connections / U-ViT-like (Bao et al. (2023))) RIN (Jabri et al. (2023)) SiD, U-ViT/2 (Hoogeboom et al. (2023)) VDM++, U-ViT/2 (Kingma & Gao (2023)) SiD2, U-ViT/1 (Hoogeboom et al. (2025))

ϵ ϵ ϵ ϵ

320M 2B 2B -

668 1110 1110 1306

x0 − ϵ x0 − ϵ x0 − ϵ

631M 682M 797M

245 311

1.79 1.62 1.61

x0 − ϵ x0 x0 x0 x0 − P ϵ x0 − M ϵ

677M 676M 953M 953M 953M 953M

5818 260 363 363 363 363

1.98 1.83 1.81 1.82* 1.79* 1.81*

#Tokens FVD↓

Tokenizer

Generator

– 32M 158M 82.2M – 173M

9.4B 321M 306M 650M 840M 343M

2065 1024 1024 1280 1280 1024

625 332 265 191 109 102

58M† ∼229M

5.5M† 467M

– 128

465 97

– – – – –

2B 458M 458M 458M 458M

– 1024 1024 1024 1024

173 111 98 97 94

Autoregressive Models CogVideo (Hong et al. (2022)) TATS (Ge et al. (2022)) MAGVIT-AR (Yu et al. (2023)) OmniTokenizer (Wang et al. (2024)) MAGVITv2-AR (Yu et al. (2024)) LARP (Wang et al. (2025)) Implicit weight-space generation

Vanilla transformers (DiT-like (Peebles & Xie (2023))) PixelFlow-XL/4 (Chen et al. (2025b)) PixelGen-XL/16 (Ma et al. (2026c)) PixelREPA-H/16 (Shin et al. (2026)) JiT-H/16 (Li & He (2026)) AsymFlow-H/16 (Chen et al. (2026a)) MF LOW-H/16 (Ours)

Params

Method

3.42 2.44 2.12 1.38

Hierarchical transformers (decoder head / DDT-like (Wang et al. (2026b))) DiP-XL/16 (Chen et al. (2026b)) DeCo-XL/16 (Ma et al. (2026b)) PixelDiT-XL/16 (Yu et al. (2026))

152 126 122

Table 5: UCF-101 video comparisons (Llevel). The rows in gray were trained by us and evaluated with individual hyperparameter tuning. † Note that we use the mapping network as generator and synthesis network as tokenizer convention from Ren et al. (2026).

Pred (±) Params GFLOPs FID↓ ϵ

169

Pixel diffusion models

Hierarchical CNNs (skip connections / U-Net-like (Ronneberger et al. (2015)) ADM-G (Dhariwal & Nichol (2021))

FVD↓

Latent diffusion models

DIGAN (Yu et al. (2022)) NeRV-Diffusion-L (Ren et al. (2026)) Pixel diffusion models VideoFusion (Luo et al. (2023)) Video JiT-L/4×8×8 (Li & He (2026)) Video AsymFlow-L/4×8×8 (Chen et al. (2026a)) Video MF LOW-L/4×8×8 (ours) + post-hoc Framewise-LPIPS (ours)

Figure 8: (Left) ConvRefiner recovers high frequency across JiT/MF LOW and model sizes B/H. (Right) The generative performance remains almost the same in this post-training.

at this scale, but MF LOW is best on every benchmark, even when compared against previous pixelspace T2I models. Figure 10 presents the benchmark progression over training iterations. We further scale MF LOW to an MMDiT-XXL/16 mixture-of-experts (MoE) model with 13B total parameters and 2.9B active parameters that achieves the best performance among all models in the comparison. Interestingly, model scaling also changes the parameterization learned by MF LOW as seen in Sec. 6, and MF LOW can leverage this capacity automatically without any manual tuning. (b) ConvRefiner: We further apply ConvRefiner as a post-training stage for text-to-image generation with MF LOWXXL. Starting from the SFT checkpoint, we train the ConvRefiner for an additional 5k steps on top of the frozen base model. As shown in Fig. 9 (right), without ConvRefiner we observe the same high-frequency deficit in the 0.5–0.7 band, even though it seems to be somewhat alleviated with increased model capacity compared to Fig. 8 (left). ConvRefiner completely closes in this gap. This also shows up visually: Fig. 9 (left) shows sharper fine-scale texture, such as the veins of the leaf. Hence, ConvRefiner also fixes the high-frequency problem at scale for text-to-image generation. Additionally, as seen in 6, ConvRefiner does not have noticable effect on text-to-image benchmark performance. 9

w/o ConvRefiner

w/ ConvRefiner

Figure 9: Visualizing effect of ConvRefiner for text-to-image generation. Here we visualize the effect of adding our post-training to MF LOW-XXL on text-to-image generations. (left) We see improved details in the leaf veins in the generated image. (right) We also note the average power gain in the high-frequency (0.5–0.7) region. We see overall improvement in texture details comparable to real image spectrum. DPG Bench 

Table 6: Comparison on text-to-image generation benchmarks. Parameter counts include only the image-generation model and exclude the text encoder. Higher is better for all metrics. Best results are in bold, and second-best results are underlined.

(



PRISM Bench

. (-

)

Figure 10: Text-to-Image scores over training steps.

GenEval ↑ DPG ↑ PRISM ↑

Model

Params

PixelDiT-T2I (Yu et al. (2026)) PixNerd-XXL/16 (Wang et al. (2026a)) PixelFlow-XL/4 (Chen et al. (2025b)) PixelGen-XXL/16 (Ma et al. (2026c)) DeCo-XXL/16 (Ma et al. (2026b)) MiniT2I-L/16 (Wang et al. (2026c))

1.3B 1.2B 882M 1.1B 1.1B 912M

0.7359 0.7015 0.6463 0.7835 0.8600 0.8822

84.58 81.61 77.90 79.62 81.96 84.66

69.6 65.7 67.6 64.7 66.5 72.9

MMDiT (JiT)-L/16-SFT* MMDiT (Asym8)-L/16-SFT* MMDiT (MF LOW)-L/16-SFT* (Ours)

1.1B 1.1B 1.1B

0.8839 0.8832 0.8843

84.65 84.61 84.70

73.6 73.9 73.9

0.8898 0.8896

86.10 86.16

75.2 75.4

MMDiT (MF LOW)-XXL/16-SFT* (Ours) 13B-MoE (2.9B active) + ConvRefiner (Ours) 13B-MoE (2.9B active)

MF LOW Ablations. We ablated multiple axes of choices for MF LOW on ImageNet B-level model. We clamp the initializations to [0.05, 0.95], as otherwise the sigmoid function will blow up M . In terms of loss parameterization we see that using uG loss over u loss significantly deteriorates performance, bringing FID from 3.66 to 4.88. Training on uG creates a trivial incentive to reduce mi toward x0 -prediction without improving the recovered transport field (Appendix A.3). Subsequently, by varying the M initialization to the normalized-variance (‘norm var’) as described in 3.2, we see slight improvement over ’asym8’ initialization, FID reduces from 3.84 to 3.80. Given that ‘norm var’ has a smoother dependence on the PCA direction’s variance, we choose it as default. We also experiment with learning-rate of M parameters, and see that having a higher learning rate multiplier seems to help a bit bringing FID down from 3.80 to 3.74. We use this final setting (init ‘norm var’, u-loss, learnable M w/ 10× lr-multiplier) as our default unless specified otherwise.

Figure 11: (Left) Increasing blocks of Conv-refiner and the weight of GAN loss helps recover high frequency. (Right) Other baselines refining does not help except DiP patch detailer(Chen et al. (2026b)). This probably reflects a convolutions bias. ConvRefiner Ablations. Our preliminary control experiment showed that JiT trained normally for 5% more epochs does not improve the frequency spectrum. In Fig. 11 (left) we investigate the effect 10

of number of blocks (b ∈ 2, 4, 8) and the weight of the adversarial loss (w ∈ 0.005, 0.01, 0.02). Firstly, we see that only using the refiner without the adversarial loss helps a bit. However, the frequency spectrum gets closer to real with more blocks and more GAN weight. Favoring a smaller lightweight network, we finally select b = 4 and w = 0.02 as our final setting. This improves pixel level details as seen in Fig. 23. Ablating the choice of refiner family (Fig. 11 (right)), we see that just finetuning the unpatchify layer or using a residual attention refiner has negligible effect. Another readily available convolutional refiner choice DiP patch-detailer(Chen et al. (2026b)) does improve the high-frequency and even overshoots with the GAN loss. However, it degrades the base JiT’s FID 3.42 to 3.90 and 4.46 respectively, bolstering our choice of ConvRefiner.

6

D ISCUSSION

Figure 12: Learned M values. Variations in the MF LOW gain curves across multiple axes: objectives – w/ vs w/o LPIPS, domains – images vs videos, representations – pixel vs latent x0 -prediction models, model capacities – 1B vs 13B-MoE. M -curve Analysis. Given the learned nature of the gain parameters mi , we analyze how they vary across objectives, domains, representations, and model capacities. In Fig. 12, we visualize the learned mi values ordered by decreasing PCA variance, which we call an M -curve. Here, mi = 0 corresponds to x0 -prediction and mi = 1 to u-prediction; the ‘norm var’ initialization is shown in gray. 1. On ImageNet (a), adding LPIPS drives all but the leading few directions toward x0 prediction while also improving FID (Table 2), suggesting less need for u-like prediction beyond the dominant PCA directions. 2. Moving to videos (b), the number of directions with non-negligible gains shrinks further, showing that the preferred parameterization varies across domains. We discuss in detail about the behaviour of LPIPS on M -curve in A.4. 3. With RAEv2 (Singh et al. (2026)) (c), whose latent model uses x0 -prediction, the gains collapse almost entirely toward zero, recovering an approximately pure x0 parameterization. Yet forcing u-prediction on a small leading subspace changes FID only marginally (Table 10), indicating that a low-rank u subspace can still be tolerated. 4. Finally, in text-to-image generation (d), increasing model capacity shifts more directions toward u-prediction. Together with the RAEv2 result, this suggests that model capacity influences how much u-prediction a model can accommodate, whereas the statistics of the data representation determine where that u-prediction is most useful. In particular, for a fixed budget of N u-predicted directions, the allocation should remain datadependent, with the leading high-variance PCA directions providing a natural choice. MF LOW can exploit increased capacity or adapt to domain change, without requiring a manually chosen rank.

7

C ONCLUSION

We revisit two design questions in vanilla pixel diffusion transformers: how their prediction parameterization should adapt to the data, and whether their minimalist architecture captures highfrequency. We introduce MF LOW, a direction-adaptive parameterization that learns a continuous 11

interpolation between clean-data and velocity prediction across principal data directions, avoiding the need for manual subspace selection, saving parameterization search cycles. Our analysis of the learned M-curves further shows that the preferred parameterization changes systematically with both data statistics and model capacity. Beyond parameterization, we identify a persistent highfrequency deficit in JiT-style models and address it with ConvRefiner, a lightweight post-hoc convolutional module that restores high-frequency statistics while preserving generative quality. Together, these results suggest that both adaptive prediction targets and explicit treatment of fine-scale signal structure are important ingredients for scaling simple pixel-space diffusion transformers. AI USE STATEMENT In this work, we used AI tools only in supporting non-research roles under author supervision. Specifically, we used it to correct grammatical errors and improve the clarity of author-written text, and to assist with software tooling. In particular, we used it for plotting and visualization code used to produce some of the figures in this paper. We did not use AI tools for research ideations, for deriving results, for designing experiments, or for generating any scientific claims. We have reviewed all the AI-assisted text and figures for correctness. R EPRODUCIBILITY STATEMENT We provide the MF LOW’s closed-form velocity-recovery rule in Sec. 3.2 and Python-like pseudocode in Sec. A.2. The post-hoc ConvRefiner is specified as an architecture figure in Fig. 7, and its training objective is provided in Section 4 and Appendix A.7. Full training and sampling configurations like optimizer, learning-rate schedule, batch size, EMA, noise schedule, and the guidance interval, guidance scale, and number of sampling steps used at evaluation, are tabulated per model in Appendix A.1. Radially-averaged power spectrum (RAPS) evaluation protocol are described in Appendix A.6. All reported metrics (FID, FVD, RAPS, GenEval, DPG, Prism) are computed with standard public implementations we cite. ACKNOWLEDGMENTS We would like to thank Harsha Walvekar, Vatsal Agarwal, Prateksha Udhayanan, Namitha Padmanabhan, and Matthew Gwilliam for their help shaping this paper.

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A

A PPENDIX

A.1

H YPERPARAMETERS

We provide our training hyperparameters in Table 7. For the ImageNet and UCF101 experiments we do not specifically change any of the base architecture, unless specified otherwise. Furthermore, we also provide evaluation time hyperparameters for these experiments in Table 8. Because the model parameterization changes over training for MF LOW and hence it is not clear if the defaults work. We report inference steps, classifier-free guidance (CFG), sampling velocity-recovery clamp σmin , and CFG Interval. We use the default JiT-B hyperparameters (Heun 50 steps, CFG 2.9, CFG Interval [0.10, 1.0], σmin = 0.04) for initial ImageNet B-level experiments to isolate the effect of training objective. For H-scale results we first conducted a coarse per-model CFG scan at σmin = 0.04, interval [0.10, 1], followed by a finer CFG×σmin grid on the strongest (LPIPS) variant. For UCF-101, we firstly observed that a smaller spatial patch size of 8 × 8 worked better than 16 × 16. For the Wan2.1 latent model we used the ‘Wan-AI/Wan2.1-T2V-1.3B-Diffusers’ VAE and a DiT based on JiT’s modern architecture. For evaluation hyperparameters, we use a two-stage search because full-scale FVD evaluation is expensive. We first run a FVD@2K grid over CFG and σmin with Heun/100 to find the basin. And then over a narrowed CFG×σmin grid around the coarse optimum we calculate the full-scale FVD@10K. On the baseline, we also found 100 steps of Heun works the best around the basin, so we use that for all the experiments. The MF LOW + post-hoc Framewise-LPIPS loss model was trained for an additional 10% epochs. (We note that, the UCF101 results in Skorokhodov et al. (2024) is evaluated at a different spatial resolution of 256 with temporal subsampling and without a publicly available codebase or checkpoint it is not comparable. Hence, we omit them.) We additionally port the three objectives to a large text-to-image (T2I) stack: a multimodal DiT (MMDiT) over a weight-free PixelVAE latent (16 × 16 pixel patchify → 768-d tokens) with a frozen Qwen3-VL-8B text encoder (hidden layers {10, 20, −1}). We train a dense 1.1B model and a 13B mixture-of-experts (2.9B active) on ∼900M images (multi-resolution 256/512) with captions, then supervised-fine-tune for 4K steps on a high-quality mixture 33.5M aesthetic-filtered images. All variants share the same natural-image patch-PCA basis (uncentered, 16 × 16) as the ImageNet models, and MF LOW again uses rational gains (c=0.05) with a 10× gain learning rate. Unlike 16

the ImageNet-H and UCF settings, we do not run a per-model CFG×σmin search for T2I. We fix a single shared sampler for all variants (DDIM, 50 steps, CFG 3.0; Table 8), so the T2I numbers reflect out-of-the-box behavior. Table 7: Configuration for our JiT / AsymFlow / MF LOW models. Architecture and optimizer follow JiT-B/L/H (Li & He (2026) Tab. 9) for image/video; the text-to-image (T2I) stack is a PixelVAElatent MMDiT. We list the settings we update. Image (ImageNet-256)

Video (UCF-101, 16×1282 )

Text-to-Image

JiT-B/H (JiT Tab. 9) 131M / 953M 16 × 16 256 (+32 in-context) 128 (B), 256 (H) – (class label) pixel 0 (B), 0.2 (H)

VideoJiT-B/L (= JiT depth/width) 131M / 458M 4×8×8 1024 256 – (class label) pixel 0

MMDiT 1.1B / 13B-MoE 2.9B act 16 × 16 (PixelVAE) res-dep. (1024 @ 512px) – (none) Qwen3-VL-8B (frozen) pixel 0

AdamW, β=(0.9, 0.95) 600 / 5 1024 2×10−4 constant {0.9996,0.9998,0.9999} logit-normal µ=−0.8, σ=0.8 bf16, no grad-clip 0.1

same 3000 / 5 512 (B), 256 (L) 1×10−4 /5×10−5 constant same same same 0.1

AdamW , β=(0.95, 0.95) 300K+4K steps / 1K 2048† 1×10−4 warmup-stable-decay 0.9995 resolution-shifted† bf16, grad-clip 1.0 0.05 (text drop)

r=8 m=λ̂/(λ̂+c), c=0.05 learnable, init ‘norm var’ velocity (u) ×10 fixed patch-PCA, ImageNet (uncentered, 16×16)

r=8 same same velocity (u) ×1 fixed tubelet-PCA, UCF-101 (uncentered, 4×8×8)

r=8 same learnable, init ‘type’ (clamp) velocity (u) ×10 fixed patch-PCA, natural img (uncentered, 16×16)

VGG, t ≥ 0.3 0.1 full frame –

VGG, t ≥ 0.3 0.2 random H/2×W/2 all 16 (framewise)

VGG, t ≥ 0.3 0.1 full frame –

Architecture Backbone Params Patch Sequence length Bottleneck Text encoder Latent Dropout Training Optimizer Epochs / warmup Effective batch Learning rate LR schedule EMA decay Time sampler Precision Class drop (CFG) AsymFlow / MF LOW AsymFlow rank MF LOW gains init MF LOW θ MF LOW loss space MF LOW gain LR mult. PCA basis LPIPS Backbone / gate Weight Spatial extent Frames

sτ Normalized time τ =t/T (with t/T =σ(z), z ∼ N (0, 1)) is warped as τ 7→ , where 1 + (s − 1) τ p
s= min N/Nref , smax , N is the latent token count (HW ·min(T, 4); images T =1), Nref =256 (16×16), and smax =6 (SD3/Hunyuan-style resolution shift). †

17

Table 8: Evaluation / sampling hyperparameters for our trained models (Tables 2, 3, 4, 5). Table 1 uses a single shared base JiT-B configuration while the rest are tuned per model. Table

Model

Solver

Steps

CFG

σmin

CFG Interval

Table 3 (ImageNet, H, tuned)

JiT-H +LPIPS AsymFlow-H +LPIPS MF LOW-H +LPIPS

Heun Heun Heun

50 50 50

2.50 2.20 2.35

0.04 0.04 0.04

[0.10, 1.0] [0.10, 1.0] [0.10, 1.0]

Video JiT-B Video AsymFlow-B Video MF LOW-B

Heun Heun Heun

100 100 100

3.0 3.5 3.5

10−5 0.04 0.04

[0, 1.0] [0, 1.0] [0, 1.0]

Video JiT-L Video AsymFlow-L Video MF LOW-L +post-hoc FW-LPIPS

Heun Heun Heun Heun

100 100 100 100

3.0 4.0 4.0 3.0

10−5 0.04 0.04 0.04

[0, 1.0] [0, 1.0] [0, 1.0] [0, 1.0]

MMDiT JiT-L +SFT MMDiT AsymFlow-L +SFT MF LOW-L +SFT MF LOW-XXL (MoE) +SFT

DDIM DDIM DDIM DDIM

50 50 50 50

3.0 3.0 3.0 3.0

10−5 0.04 0.04 0.04

[0, 1.0] [0, 1.0] [0, 1.0] [0, 1.0]

Table 4 (UCF, B, tuned)

Table 5 (UCF, L, tuned)

∗

Tables 3 (T2I, shared)

18

A.2

MF LOW I MPLEMENTATION D ETAILS

All operators are diagonal in the fixed patch-PCA basis U , so every step is a change of basis (img→patch coeffs @ U), a per-direction scalar op, and a change back (@ U⊤ → img). Below, x is a batch of patch-token tensors, t∈[0,1] is flow matching timestep, U (D,D) and lam (D,) are the precomputed PCA basis/variances. These mirror the JiT codebase. # One-time setup: fixed gains from lambda, or learnable # params. lam_n is the normalized variance (lam_max = 1). def setup_gains(lam): lam_n = lam.clamp(min=0) / lam.clamp(min=0).max() m_fixed = lam_n / (lam_n + c) return m_fixed # Learnable variant (default): phi (D,) logits + scalar # m_i = sigmoid(phi_i). def gains(): if learnable: m = sigmoid(phi) # phi is init with torch.logit(m_fixed) else: m = m_fixed return m

# Graded target u_G = x0 - M eps (Using Eq.2), in the PCA basis. def mflow_target(x0, eps, t): m = gains() ce = to_patch_coeffs(eps) @ U # eps in PCA coords Me = (m * ce) @ U.T # M eps = U diag(m) UˆT eps return x0 - to_img(Me) # u_G

# Exact recovery of x0-hat from the output u_G (Using Eq.5, Using Eq.6). def mflow_to_x0(u_M, x_t, t): m = gains(t) omt = clamp_min(1 - t, t_eps) # (1 - t) cu = to_patch_coeffs(u_M) @ U # u_M coeffs cz = to_patch_coeffs(x_t) @ U # x_t coeffs denom = clamp_min(omt + m * t, t_eps) # Delta_i = (1-t)+m_i t x0_c = (omt * cu + m * cz) / denom # x0-hat coeffs (eq. 11) return to_img(x0_c @ U.T)

# Velocity for sampling (Using Eq.6). def mflow_to_velocity(u_M, x_t, t): x0_hat = mflow_to_x0(u_M, x_t, t) return (x0_hat - x_t) / clamp_min(1 - t, t_eps)

# Training step: velocity-space flow-matching loss. def training_loss(net, x0, t): eps = randn_like(x0) x_t = t * x0 + (1 - t) * eps # forward interpolant u_M = net(x_t, t, cond) # raw output ˜= u_G u_pred = mflow_to_velocity(u_M, x_t, t) # -> full velocity loss = weight(t) * mse(u_pred, x0 - eps) # Using Eq.7 return loss

# Sampling: Euler/Heun on velocity, integrating t: 0 -> 1.

19

def sample(net, steps): x = randn(...) # t = 0, pure noise for t0, t1 in schedule(steps): u = mflow_to_velocity(net(x, t0, cond), x, t0) x = heun_step(x, u, t0, t1, net) return x

A.3

W HY MF LOW U SES u- PREDICTION

MF LOW predicts the graded target uG = x0 − M ϵ,

(8)

where the direction-wise gains mi = sigmoid(ϕi ) are optimized jointly with the network. A natural alternative would be to directly regress this target: i h 2 (9) LG (θ, ϕ) = E w(t)∥ûG − uG ∥2 . Here, uG is not detached from the computation graph, so this objective does propagate gradients to the gains. We show, however, that it introduces an undesirable dependence on the scale of the chosen parameterization. Recall that xt = tx0 + (1 − t)ϵ,

u = x0 − ϵ.

(10)

∆i (t) := (1 − t) + tmi .

(11)

In PCA direction i, the graded target can be rewritten as ũG,i = (1 − mi )x̃t,i + ∆i (t)ũi ,

ˆG,i is Consequently, the velocity recovered from a network prediction ũ ˆ ˆi = ũG,i − (1 − mi )x̃t,i . ũ ∆i (t)

(12)

Combining Eqs. equation 11 and equation 12 gives the exact error relation   ˆi − ũi . ˆG,i − ũG,i = ∆i (t) ũ ũ

(13)

Thus, direct graded-target supervision is equivalent to " #  2 X 2 ˆ LG = E w(t) ∆i (t) ũi − ũi .

(14)

i

The same recovered-velocity error therefore receives a different penalty depending on mi and t. The gains receive gradients. Because the target is not detached, the per-sample derivative of the direct loss is   ∂ℓG,i ˆG,i − ũG,i ϵ̃i . = 2w(t) ũ (15) ∂mi ũˆG,i Equivalently,   ∂ℓG,i ˆG,i − ũG,i ϵ̃i mi (1 − mi ). = 2w(t) ũ (16) ∂ϕi This gradient is generally nonzero, but its sign depends on the current prediction residual. The issue with direct supervision is therefore not that the gains cannot learn, but that the objective admits a parameterization-scale shortcut. ¯i (xt , t). For A parameterization-scale shortcut. Consider any fixed recovered-velocity predictor ũ every value of mi , define the corresponding graded prediction ˆ(mi ) = (1 − mi )x̃t,i + ∆i (t)ũ ¯i . ũ G,i 20

(17)

Substituting Eq. equation 17 into the recovery map always yields the same predictor: ˆ(mi ) − (1 − mi )x̃t,i ũ G,i ∆i (t)

¯i . = ũ

(18)

Hence, changing mi along this family does not change the recovered transport field. Nevertheless, the direct graded-target loss becomes ¯i − ũi )2 . ℓG,i (mi ) = w(t) ∆i (t)2 (ũ

(19)

Its derivative along this equivalent-predictor family is dℓG,i ¯i − ũi )2 ≥ 0. = 2w(t) t ∆i (t)(ũ dmi

(20)

Therefore, whenever t > 0 and the recovered velocity has nonzero error, decreasing mi reduces the graded-target loss while leaving the recovered velocity unchanged. The direct objective can thus improve by making the target more x0 -like, rather than by learning a more accurate transport field. This does not imply that every instantaneous minibatch gradient must decrease mi . Instead, Eq. equation 20 shows that the joint optimization problem contains a loss-reducing direction that is unrelated to transport accuracy. For the binary AsymFlow parameterization,  1, ∆i (t)2 = (1 − t)2 ,

mi = 1, mi = 0.

(21)

Direct uG supervision therefore suppresses recovered-velocity errors in the clean-image-prediction subspace by (1 − t)2 . Near the clean endpoint, t → 1, these errors become almost unpenalized, even though they are amplified when the prediction is converted back to velocity. Velocity-space supervision. MF LOW instead applies the standard flow-matching objective after exact velocity recovery: " # 2 X ˆi − ũi Lu (θ, ϕ) = E w(t) ũ . (22) i

Using Eq. equation 13, this is equivalently 

 2  ˆ X ũG,i − ũG,i   Lu = Ew(t) . ∆i (t)2 i

(23)

The inverse factor from velocity recovery cancels the artificial ∆i (t)2 scaling of the graded target. In particular, along the equivalent-predictor family in Eq. equation 17, i d h ¯i − ũi )2 = 0. w(t)(ũ (24) dmi Velocity-space supervision therefore evaluates all parameterizations using the same transport objective. The gains can still adapt because they alter the conditioning and finite-capacity approximation problem faced by the network, but they cannot reduce the objective merely by shrinking the scale of the regression target. A.4

S URPRISING BEHAVIOUR LPIPS ON THE L EARNED M -C URVE

Figure 12(a) shows that LPIPS substantially changes the prediction parameterization learned by MF LOW. Without LPIPS, the gains decrease approximately monotonically with PCA variance: high-variance directions receive more u-like prediction, while lower-variance directions become increasingly x0 -like. This behavior is consistent with the normalized-variance initialization. With LPIPS, however, the leading gains become non-monotonic. Using zero-based indexing, PC0 and PC1 retain high gains, PC2–PC3 exhibit a pronounced dip, and PC4 rises again. 21

Figure 13: Leading modes of the uncentered patch-PCA basis. We reshape the first 64 eigenvectors of the 16 × 16 × 3 patch-PCA basis into RGB patches; the value λ denotes the variance of each direction. The leading ordering interleaves patch-global or very low-frequency modes with spatially varying modes. In particular, PC0 is dominated by low-frequency patch-level tone, PC1 is an approximately uniform chromatic mode, PC2–PC3 encode spatial gradients, and PC4 returns to an approximately uniform chromatic mode. Eigenvector signs are arbitrary, so the interpretation is based on spatial structure rather than the displayed color polarity. The PCA modes in Fig. 13 provide a structural interpretation of this pattern. PC0 represents a patch-global, low-spatial-frequency component, while PC1 is nearly constant across the patch and primarily changes its color. In contrast, PC2 and PC3 contain vertical and horizontal spatial gradients. PC4 then returns to a nearly spatially uniform chromatic component. The leading sequence is therefore approximately patch-global,

patch-global,

spatial,

spatial,

patch-global,

which closely matches the learned gain pattern high,

high,

low,

low,

high.

In particular, PC4 has substantially lower variance than PC2 and PC3 (λ4 = 3.74, compared with λ2 = 9.41 and λ3 = 7.93), yet LPIPS assigns it a larger gain. The spike at PC4 is therefore not explained by variance ordering alone; it coincides with the return of a patch-global chromatic mode after two spatial-gradient modes. This effect is also more specific than a preference for color. Several later PCA directions contain strong chromatic variation but are spatially non-uniform, and they do not receive the same gain increase. The observed pattern instead suggests that LPIPS distinguishes between patch-global tone or color changes and spatially varying patterns. One possible explanation follows from the conditional-mean behavior of squared-error regression. In a finite-capacity model, a more x0 -like parameterization can shrink uncertain components toward their conditional means. For a spatially varying component, such shrinkage may primarily smooth a local gradient or texture. For a patch-global component, however, it can coherently alter the brightness, contrast, or color of the entire patch. Because LPIPS is applied to the recovered clean image, it may make these perceptually coherent shifts more costly. The learned parameterization responds by retaining a larger velocity-like component for the patch-global modes, thereby reducing their tendency toward mean reversion. The controlled comparison establishes that adding LPIPS produces the non-monotonic M -curve and that the unusually high gains align with patch-global PCA modes. The mean-reversion explanation is a plausible interpretation of this alignment rather than a causal mechanism directly established by the ablation. A.5

A C APACITY-C ONSTRAINED V IEW OF x0 - AND u-P REDICTION

The choice between clean-data and velocity prediction involves two competing considerations. Clean-data prediction avoids asking the model to reproduce full-dimensional Gaussian noise, which can be advantageous when a high-dimensional representation has much lower intrinsic dimension. 22

Velocity prediction, on the other hand, provides better numerical conditioning near the clean endpoint. Our RAEv2 experiment illustrates this trade-off particularly clearly. RAEv2 predominantly favors clean-data prediction. In our clean-latent RAEv2 setup, the pure x0 -prediction baseline obtains an FID of 1.05, while AsymFlow with r = 8 and MFlow obtain 1.08 and 1.09, respectively, after 80 epochs (Table 10). Consistently, the learned MFlow gains in Fig. 12(c) move almost entirely toward zero, recovering an approximately pure x0 parameterization. These results indicate that, for this representation, model, and training budget, the network prefers to avoid predicting noise in most latent directions. At the same time, the AsymFlow result is only 0.03 FID behind the pure-x0 baseline, despite using full velocity prediction in its leading eight PCA directions. This result does not show that velocity prediction is superior in this setting; pure x0 -prediction remains best in Table 10. It instead shows that a small velocity-prediction subspace can be accommodated at little measured cost, even in a representation that strongly favors x0 -prediction overall. Numerical conditioning versus target complexity. The benefit of retaining a velocity-like component can be understood from the recovery map. Under our convention, xt = tx0 + (1 − t)ϵ,

t = 1 is the clean endpoint.

For pure x0 -prediction, the velocity is recovered as ˆ ˆi = x̃0,i − x̃t,i . ũ 1−t

(25)

ˆ0,i − x̃0,i in the clean-data prediction produces a velocity error Consequently, an error δix = x̃ x ˆi − ũi = δi . ũ 1−t

(26)

The factor 1/(1 − t) becomes ill-conditioned as t → 1. For MFlow, the corresponding relation is ˆ ˆi − ũi = ũG,i − ũG,i , ũ ∆i (t)

∆i (t) = (1 − t) + tmi .

(27)

When mi = 0, this reduces to the same 1/(1 − t) amplification as x0 -prediction. For any mi > 0, however, lim ∆i (t) = mi , t→1

so the clean-endpoint singularity is removed in that direction. Thus, conditional on comparable target-prediction errors, a nonzero velocity component gives better-conditioned velocity recovery near clean samples. This conditioning advantage comes with an opposing cost. Increasing mi changes the target from clean-data prediction toward ũG,i = x̃0,i − mi ϵ̃i , requiring the finite-capacity network to retain a larger Gaussian-noise component. Full velocity prediction is therefore well conditioned during recovery but can be difficult to approximate in highdimensional spaces, whereas pure x0 -prediction removes the noise-prediction burden but retains the clean-endpoint amplification. The optimal parameterization must balance these two effects. A soft velocity budget. This trade-off suggests viewing MFlow as learning both how much velocity prediction the model can support and where it should be allocated. A useful summary of the former is the soft velocity rank X reff := tr(M ) = mi . (28) i

Pure x0 -prediction has reff = 0, full u-prediction has reff = D, and rank-r AsymFlow has reff = r. For MFlow, this quantity is continuous and learned. Our results suggest a capacity-constrained principle: use velocity-like prediction in as many directions as the model can accurately support, and retain clean-data-like prediction in the remaining 23

Table 9: Learnable gains on UCF-101 (Blevel). Results use the default sampling hyperparameters, without an evaluation sweep. Method

FVD↓

Video MF LOW, fixed gains Video MF LOW, learnable gains

169.4 155.5

Table 10: RAEv2 results. H-level models trained on ImageNet for 80 epochs. Method

FID↓

RAEv2 Singh et al. (2026) RAEv2 + Asym8 RAEv2 + MF LOW

1.05 1.08 1.09

directions. The RAEv2 curve indicates a small velocity budget for this high-dimensional latent representation, whereas the text-to-image curves show that increasing model capacity shifts more directions toward velocity prediction. We therefore interpret model capacity as influencing the available velocity budget, while the data representation and training objective determine how that budget should be distributed. Why leading PCA directions are a natural default. Suppose that only N directions can be assigned substantial velocity gains. In the absence of perceptual or other auxiliary losses, the leading PCA directions provide a natural initial allocation. In the PCA basis, Var(x̃0,i ) = λi ,

Var(ϵ̃i ) = 1,

(29)

where λi decreases with i, while the isotropic noise variance is identical in every direction. The velocity target therefore becomes increasingly noise-dominated as λi decreases. Allocating a limited velocity budget to high-variance directions concentrates the noise-prediction burden in the dominant data subspace, while keeping the many low-variance, predominantly off-manifold directions closer to x0 -prediction. It also improves near-clean conditioning in the directions carrying the largest fraction of the data variation. This PCA ordering should nevertheless be viewed as an initialization prior rather than a universal rule. Auxiliary objectives can favor directions according to their visual function rather than variance, as shown by the non-monotonic LPIPS M -curve in Fig. 12(a). We also observe that a non-leading PCA block can outperform the first eight directions in one ImageNet pilot. MFlow therefore initializes gains using normalized variance but lets the model modify both the effective velocity budget and its direction-wise allocation through end-to-end training. A.6

R ADIALLY-AVERAGED P OWER S PECTRUM

To quantify how faithfully a model reproduces the spatial-frequency content of natural images, we compare the azimuthally-averaged 2D power spectrum of generated and real images. Each image is converted to luma (Y = 0.299R + 0.587G + 0.114B), mean-subtracted to remove the DC component, and multiplied by a separable 2D Hann window to suppress boundary leakage. We compute the squared magnitude of its 2D DFT, P (f ) = |F g(f )|2 , center it (fftshift), and azimuthally average it, i.e., average over all orientations at each fixed radius r = ∥f ∥, to obtain a 1D profile P (f ) as a function of radial frequency f (cycles/pixel). Averaging P (f ) over N = 4000 images gives the RAPS of a distribution. A.7

R EFINERS

For our ConvRefiner we use a t-conditioned PatchGAN discriminator (Isola et al. (2017)) (NLayerDiscriminator, 3 layers, ndf=64) with a hinge adversarial loss, applied to the refined x̂0 . We have two types of batches – all-t batch and near-clean batch (t ∼ U(0.9, 0.98)). For the all-t batch the flow-matching and LPIPS(t ≥ 0.3) losses are normally applied. For the near-clean batch, additional GAN loss is applied with a 0.02 weight, if not otherwise specified, and the flow-matching and LPIPS loss are downweighted by a factor of 0.25. For Attention Refiner we used a 2 blocks of swin-style (Liu et al. (2021)) windowed attention residual refiner in the clean image space, as a drop in replacement for the ConvRefiner. Note that DiP patch-detailer also takes as input xt apart from the model output. A.8

L IMITATIONS .

Although MF LOW is a general formulation that transfers across pixel-space image and video generation, high-dimensional representation latents such as RAEv2 Singh et al. (2026), and text-to-image 24

Figure 14: ImageNet Loss Curves at H-level. We usually observe that the u-loss of MF LOW training is very slightly better.

Figure 15: Faster convergence on ImageNet with LPIPS at B-level. This corresponds to the results noted in Table 2. models of different capacities, its improvements over strong fixed parameterizations are sometimes modest. One possible reason is the joint optimization of the gains and network weights. While the underlying velocity target remains fixed, updating M continuously changes the network’s direct output parameterization uG = x0 − M ϵ, creating an effectively moving regression target and allowing the gains and network to co-adapt. Indeed, under the same velocity-space objective, MF LOW attains a slightly lower training loss than JiT and AsymFlow on the ImageNet H-level experiment (Fig. 21); we observe similar trends for B-level models with and without LPIPS. However, the lower diffusion loss does not consistently translate into better FID. This mismatch suggests that improved regression conditioning need not directly improve distribution-level sample quality, and its precise cause remains unclear. Staged or decoupled optimization of the gains is an important direction for future work. ConvRefiner reveals a complementary evaluation limitation. It substantially closes the highfrequency spectral gap and brings the generated spectrum closer to that of real images, yet this improvement produces little or no change in FID. This suggests that FID is relatively insensitive to the local frequency statistics modified by the refiner. Consequently, spectral fidelity and FID should be viewed as complementary rather than interchangeable measures; texture-sensitive metrics and human evaluation are needed to determine how strongly the recovered high-frequency content translates to perceived image quality.

25

Figure 16: Qualitative Text-to-Image Results on DPG-Bench. Images generated by our method and baselines on DPG-Bench prompts.

26

MMDiT- MFlow (L/16)

MMDiT- Asym8 (L/16)

MMDiT- JiT (L/16) MiniT2I (L/16)

DeCo (XXL/16)

PixelGen (XXL/16)

PixelFlow (XL/4) PixelNerd (XXL/16)

PixelDiT-T2I

An image showcasing an individual with a smartphone in their left hand, positioned right next to a pair of black-framed glasses resting upon a table. The person in the scene, clearly engrossed in their device, is wearing a textured dark jacket, suitable for chilly weather. Above them, a clear blue sky stretches expansively, uninterrupted by any visible obstacles or elements.

An aerial view of a coastal French city, captured in a satellite image, reveals a sprawling green park on the western edge, bordered by neatly arranged streets. To the north, a majestic mountain looms over the urban landscape, its peak just touching the edges of a drifting cloud that partially obscures the view. The intricate patterns of the city's layout are visible, with residential areas, winding roads, and the shimmering coastline all distinctly marked from this bird's-eye perspective.

a spacious square where a large, weathered stone pedestal stands prominently at the center, devoid of the horse statue that once adorned it. The pedestal's surface is rough and covered with patches of moss, indicating its age and exposure to the elements. Around the base, cobblestones are laid in a pattern that radiates outward, suggesting the importance of the now-absent statue.

A close-up image of an intricately designed lotus flower, which appears to be crafted entirely from crystal-clear water droplets. The flower is set against a backdrop of soft green lily pads floating on a tranquil pond. Sunlight filters through the scene, highlighting the delicate texture and the shimmering surface of the water-formed petals.

a detailed oil painting depicting a ginger cat with green eyes, intently focused on a game of checkers. The cat is seated at a small wooden table, with the checkerboard laid out in front of it, pieces strategically placed. The painting captures the texture of the cat's fur and the wood grain of the table, set against a soft, neutral background that draws attention to the subject.

MMDiT- MFlow (XXL/16)

Figure 17: Qualitative Text-to-Image Results on PRISM-Bench. Images generated by our method and baselines on PRISM-Bench prompts.

27

MMDiT- MFlow (L/16)

MMDiT- Asym8 (L/16)

MMDiT- JiT (L/16) MiniT2I (L/16)

DeCo (XXL/16)

PixelGen (XXL/16)

PixelFlow (XL/4) PixelNerd (XXL/16)

PixelDiT-T2I

Radiant joy and youthful exuberance shine through a playful haircut, symbolizing the boundless freedom and innocence of childhood.

Lindsey Wixson stands confidently in a golden wheat field, donning a wide-brimmed straw hat, bold red sunglasses, and a vibrant red fur-trimmed top, accessorized with a sparkling diamond necklace, embodying summer elegance.

Two joyful children, accompanied by a playful puppy, explore a vibrant forest trail filled with blooming yellow flowers and towering trees, embodying the spirit of adventure and friendship.

Castle Rock in Sedona, Arizona, stands as a silent sentinel of eternity, its rugged forms piercing the sky like ancient sentinels, while the vibrant greenery below whispers tales of resilience and renewal, inviting contemplation amidst the timeless embrace of nature.

Embracing the warmth of rustic charm, this cabin invites serenity and introspection, where the crackling fire whispers stories of comfort, the soft textures of wood evoke a timeless connection to nature, and the gentle breeze through the windows carries the promise of peace and renewal.

MMDiT- MFlow (XXL/16)

Figure 18: Qualitative ImageNet Results. Images generated by MF LOW +ConvRefiner H-level model.

28

Figure 19: More Class-wise Uncurated Qualitative ImageNet Results. Images generated by MF LOW +ConvRefiner H-level model.

29

Figure 20: More Class-wise Uncurated Qualitative ImageNet Results. Images generated by MF LOW +ConvRefiner H-level model.

30

Figure 21: Qualitative UCF-101 Results. Frames generated by MF LOW +post-hoc FW-LPIPS L-level model.

31

Figure 22: Visualizing effect of ConvRefiner. Here we visualize the effect of adding our posttraining to MF LOW-H+LPIPS on ImageNet generations. We also note the average power gain in the high-frequency(0.5–0.7) region. We see overall improvement in texture details.

32

JiT+LPIPS base

ConvRefiner b4+GAN(w.02) +12.2dB

|b4-base|

ConvRefiner b8+GAN(w.02) +13.7dB

+10.4dB

+13.4dB

+10.4dB

+12.2dB

+10.8dB

+11.2dB

+7.4dB

+8.7dB

|b8-base|

Figure 23: Qualitative Ablation for ConvRefiner. Here we visualize the effect of adding our post-training to JiT-B on ImageNet generations. We also note the average power gain in the highfrequency(0.5–0.7) region. We also show the visual improvements – we see that b4 adds additional texture details, while b8 sometimes overshoots in texture. 33

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