Related papers: Faster Diffusion Sampling with Randomized Midpoint…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
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 applications in machine learning, physics, statistics, etc. In…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
Diffusion models have achieved remarkable success in generating high-fidelity content but suffer from slow, iterative sampling, resulting in high latency that limits their use in interactive applications. We introduce DRiffusion, a parallel…
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Diffusion models have emerged as state-of-the-art generative models for image generation. However, sampling from diffusion models is usually time-consuming due to the inherent autoregressive nature of their sampling process. In this work,…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms,…
Sampling from multiple distributions so as to maximize overlap has been studied by statisticians since the 1950s. Since the 2000s, such correlated sampling from the probability simplex has been a powerful building block in disparate areas…
Recent diffusion distillation methods have achieved remarkable progress, enabling high-quality ${\sim}4$-step sampling for large-scale text-conditional image and video diffusion models. However, further reducing the number of sampling steps…
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining…
We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a…
Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling…
Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…
We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and…
Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plateau in performance while SDE-based samplers deliver higher…
We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new convergence guarantees under weaker assumptions than strong log-concavity: namely, our results hold for (1) weakly log-concave targets, and (2) targets satisfying…
Diffusion models play a pivotal role in contemporary generative modeling, claiming state-of-the-art performance across various domains. Despite their superior sample quality, mainstream diffusion-based stochastic samplers like DDPM often…
Discrete diffusion language models (dLLMs) have recently emerged as a promising alternative to traditional autoregressive approaches, offering the flexibility to generate tokens in arbitrary orders and the potential of parallel decoding.…