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.
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arXiv:2607. 23226v1 Announce Type: new Abstract: Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped.
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: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: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: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.
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.