The paper investigates the relationship between the Föllmer process—a Brownian motion conditioned to reach a specified distribution at time 1—and the denoising diffusion probabilistic model (DDPM). It demonstrates that discretizing the Föllmer process yields natural hyper‑parameter settings for the DDPM sampler and supports a wider range of variance schedules than discretized reverse SDEs. By leveraging this connection, the authors systematically recover state‑of‑the‑art DDPM sampling error bounds and achieve slight improvements.
arXiv:2608. 02799v1 Announce Type: cross Abstract: Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus.
arXiv:2609.00279v1 Announce Type: cross Abstract: This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional t...
arXiv:2505. 06800v2 Announce Type: replace-cross Abstract: Diffusion-based generative models have renewed interest in stochastic differential equation methods for sampling from complex distributions.
The paper establishes a first‑order theoretical framework for diffusion models, showing that SDE‑based reverse‑time flows of both overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponential rates when the stationary potential of the forward process is strongly convex. It further incorporates discretization to provide averaged first‑order stationarity bounds—sampling analogues of averaged gradient‑norm guarantees in nonconvex optimization—for samplers of both diffusion models. These results highlight a unique advantage of SDE‑based reverse diffusion over ODE‑based approaches, offering local convexity‑free certificates that ensure score consistency rather than global mode weights.
Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al.
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.
arXiv:2502. 08834v4 Announce Type: replace-cross Abstract: Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks.
arXiv:2605. 00161v2 Announce Type: replace Abstract: Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps.
The paper proves that for discrete diffusion models using uniform or remasking forward processes, an adaptive sampler based on a leave‑one‑out denoiser can achieve sampling error proportional to the score‑estimation error plus a small tolerance. The required number of discretization steps scales with the dual total correlation of the target distribution, not directly with the ambient dimension. This result shows that sampling complexity is governed by the intrinsic dependence structure of the distribution, and the authors provide an information‑theoretic analysis linking discretization error to mutual information between coordinates.
arXiv:2606. 02115v1 Announce Type: cross Abstract: Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields.
arXiv:2506. 13061v4 Announce Type: replace Abstract: Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise.