Official Review · ICLR 2025

The authors explore training diffusion bridges with the following focus: - investigating the case where the reference diffusion process has degenerate noise - explores the under-damped Langevin case - numerical experiments The authors explore underdamped diffusions for sampling and appear to achieve record performance in Table 1, Figure 3 etc. compared to the baselines considered for the datasets considered, including some medium dimensional data d>1000. The authors explore a variety of known splitting based sampling schemes to improve performance. This appears under-explored in the literature of diffusion models. The authors claim their method enables end-to-end hyper-parameter tuning. This appears to be a novel and valuable contribution though I do not understand how this works and it does not appear well explained in the paper (as detailed in weaknesses below). It is not clear to me what the contributions are in this submission nor the significance. It appears most of the propositions/ theorems are from other works. The authors claim that the novelty in this work is extending these to the degenerate noise case. It is not clear to me why the degenerate noise case is useful or important (bullet 1 of contributions). >Even though for (underdamped) diffusion models with degenerate η, a corresponding (hybrid) score matching loss has been suggested by Dockhorn et al. (2021), it has so far been unclear whether it can also be connected to an ELBO, i.e., to likelihood optimization. Likelihood based training for underdamped diffusion models has indeed been investigated in Dockhorn et al. (2021), see e.g. sections "B.3 CLD OBJECTIVE"; "F.1.2 MAXIMUM LIKELIHOOD TRAINING". (bullet 2 of contributions). > Novel underdamped samplers: Splitting based samplers have been used before, as cited by the authors e.g. Monmarché · 2021. It is claimed by the authros (bullet 3 of contributions) that these samplers are novel. Is the novelty in using these for sampling with diffusions? I appreciate these splitting methods have been used before with damped diffusions and for diffusion models, but the full design space has not been explored. The promise of end-to-end training is very attractive (bullet 4 of contributions). How is this achieved in practice? It appears this is only discussed in the numerical experiments yet is one of the main selling points of this work. Can the authors elaborate more on this? It appears from Figure 5 that learning hyper parameters is key to good performance. The simulation based loss considered appears to be the same as that proposed in "Guided proposals for simulating multi-dimensional diffusion bridges", [1] for forward KL eqn (9) and (11). If I understand correctly, this requires simulating the whole diffusion trajectory under some discretisation to learn the drift and has been considered by [1] for simple drift terms. The approach by [2] requires simulating in the nonlinear diffusion case up to time t and not the whole trajec