The paper investigates training diffusion models to sample from distributions defined by unnormalized densities or energy functions. It benchmarks various diffusion-structured inference techniques, including simulation-based variational methods and off-policy approaches such as continuous generative flow networks, highlighting their relative strengths and challenging some prior claims. Additionally, the authors introduce a new exploration strategy for off-policy methods that employs local search in the target space with a replay buffer, demonstrating improved sample quality across multiple target distributions.
By Marcin Sendera, Minsu Kim, Sarthak Mittal, Pablo Lemos, Luca Scimeca, Jarrid Rector-Brooks, Alexandre Adam, Yoshua Bengio, Esmeralda S. Whitammer
arXiv:2602.15396v2 Announce Type: replace
Abstract: Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces in...
By Jeongwoo Shin, Jinhwan Sul, Joonseok Lee, Jaewong Choi, Jaemoo Choi
arXiv:2509.26364v3 Announce Type: replace
Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
By Kirill Tamogashev, Esmeralda S. Whitammer
arXiv:2511. 06239v2 Announce Type: replace-cross Abstract: Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited.
By Byoungwoo Park, Juho Lee, Guan-Horng Liu
The paper examines the common practice in diffusion and flow matching of predicting the clean signal, converting it to a velocity, and training with a velocity-space loss. It shows that this conversion can cause unstable optimization due to singular endpoint amplification, but that prediction–loss alignment removes this source of non‑integrability and ensures a finite second moment for all timesteps, even with uniform sampling. Experiments confirm that aligned objectives remain trainable across different samplers, reconciling theoretical concerns with empirical success.
By Jiadong Hong, Lei Liu, Xinyu Bian, Wenjie Wang, Zhaoyang Zhang
arXiv:2607. 14398v1 Announce Type: cross Abstract: Constrained generative models aim to produce samples that satisfy complex feasibility constraints while remaining faithful to the data distribution.
By Xiaoxuan Liang, Saeid Naderiparizi, Berend Zwartsenberg, Frank Wood