The paper presents new Kullback–Leibler convergence guarantees for score diffusion models that avoid restrictive Lipschitz assumptions on the score function. By analyzing models with fixed step size derived from the Ornstein–Uhlenbeck semigroup and its kinetic counterpart, the authors derive simple, sharp KL bounds that hold for any data distribution with finite Fisher information relative to the standard Gaussian. This extends theoretical guarantees to a broader class of data distributions without requiring early stopping or compact support.
arXiv:2511. 05940v3 Announce Type: replace-cross Abstract: Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains.
arXiv:2607. 04442v1 Announce Type: cross Abstract: Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution.
arXiv:2609.27546v1 Announce Type: cross Abstract: Score-based diffusion models are increasingly considered in settings where the underlying data distribution may differ from the training distribution...
arXiv:2506. 11378v3 Announce Type: replace Abstract: Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary stochasticity function or a probability flow ODE, corresponding to setting this stochasticity function to zero.
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.
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.
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.
The paper establishes finite‑sample guarantees for fully discrete conditional diffusion models trained from data and run with a finite number of denoising steps. By aligning the score‑training objective with the sampling grid, the authors jointly analyze statistical estimation and numerical discretization errors. For any smoothness index β>0, they prove that an appropriately chosen grid yields an averaged conditional Kullback–Leibler divergence of ˗O_p(n^{-2β/(d_x+d_y+2β)}) and a total‑variation error of ˗O_p(n^{-β/(d_x+d_y+2β)}), matching known rates up to logarithmic factors.
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.
arXiv:2605. 17232v2 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology.
arXiv:2605. 17232v5 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology.
arXiv:2610.07655v1 Announce Type: cross Abstract: Discrete diffusion models have emerged as a practically successful framework for generative modeling on discrete product spaces, yet their statistica...