We provide theoretical convergence guarantees for score-based generative models (SGMs)
such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of …

Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

It is a fundamental problem to understand the complexity of high-accuracy sampling from a
strongly log-concave density π on ℝ d. Indeed, in practice, high-accuracy samplers such as …

We study the mixing time of the Metropolis-adjusted Langevin algorithm (MALA) for
sampling from a log-smooth and strongly log-concave distribution. We establish its optimal …

We study the complexity of sampling from the stationary distribution of a mean-field SDE, or
equivalently, the complexity of minimizing a functional over the space of probability …

We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its
convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas …

Langevin diffusions are rapidly convergent under appropriate functional inequality
assumptions. Hence, it is natural to expect that with additional smoothness conditions to …

We propose a sampling algorithm that achieves superior complexity bounds in all the
classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI) …

Given a convex function $ f\colon\mathbb {R}^{d}\to\mathbb {R} $, the problem of sampling
from a distribution $\propto e^{-f (x)} $ is called log-concave sampling. This task has wide …

In light of the widespread success of generative models, a significant amount of research
has gone into speeding up their sampling time. However, generative models are often …