The paper addresses the challenge of guiding conditioned generative models that are diffusion processes with singular diffusion coefficients, where traditional conditional densities may be nonexistent or non‑smooth. It proposes using causal optimal transport to construct approximate loss functions that identify a minimum‑entropy control for guidance, relying on the predictable representation property of conditioned diffusion processes and well‑posed martingale problems à la Üstünel.
arXiv:2602. 05533v3 Announce Type: replace Abstract: We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one.
By Zhengyi Guo, Wenpin Tang, Renyuan Xu
arXiv:2606. 13240v1 Announce Type: cross Abstract: A key strength of diffusion models lies in their flexibility, since their outputs can be controlled at sampling time through guidance.
By Rapha\"el Razafindralambo, R\'emy Sun, Fr\'ed\'eric Precioso, Jes Frellsen, Pierre-Alexandre Mattei
arXiv:2608. 03117v1 Announce Type: new Abstract: The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions.
By Kentaro Kaba, Masayuki Ohzeki, Yuki Sughiyama
arXiv:2607. 10067v1 Announce Type: new Abstract: While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives.
By Ziv Aharoni, Henry D. Pfister
arXiv:2608. 19504v1 Announce Type: new Abstract: We propose a conditioning mechanism for diffusion models based on multi-speed joint diffusion of the target and the condition.
By Libo Chen, Souvik Ghosh, Teo Deveney, Chris Budd, Vinay P. Namboodiri
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2606. 16610v1 Announce Type: cross Abstract: Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood.
By Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus
Uniform discrete diffusion models (UDMs) typically rely on explicit time conditioning, yet this study finds that such conditioning is often unnecessary in practice. While the population‑optimal UDM predictor generally depends on time—controlling how much the model should trust the observed context—the dependence becomes negligible in finite‑data language settings. Empirical results show that trained language UDMs exhibit limited time sensitivity across most of the diffusion trajectory, and time‑agnostic predictors can match or outperform time‑conditioned models on various datasets and training objectives.
By Chunsan Hong, Chieh-Hsin Lai, Satoshi Hayakawa, Yuhta Takida, Jong Chul Ye, Yuki Mitsufuji
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:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
By Lei Luo, Yingzhen Zhang, Jian Yang