Related papers: High-accuracy sampling for diffusion models and lo…
We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
We consider the problem of sampling from a log-concave distribution $\pi(\theta) \propto e^{-f(\theta)}$ constrained to a polytope $K:=\{\theta \in \mathbb{R}^d: A\theta \leq b\}$, where $A\in \mathbb{R}^{m\times d}$ and $b \in…
In large-data applications, such as the inference process of diffusion models, it is desirable to design sampling algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of sampling, which is the…
We study the problem of estimating multivariate log-concave probability density functions. We prove the first sample complexity upper bound for learning log-concave densities on $\mathbb{R}^d$, for all $d \geq 1$. Prior to our work, no…
In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution…
We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…
We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…
Score-based diffusion models have achieved remarkable empirical success in generating high-quality samples from target data distributions. Among them, the Denoising Diffusion Probabilistic Model (DDPM) is one of the most widely used…
We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.e., densities of the form $\pi\propto e^{-f-g}$, assuming access to gradient evaluations of $f$ and a restricted Gaussian oracle (RGO) for…
This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Denoising Diffusion Monte Carlo (DDMC), based on the simulation of a denoising…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…
This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Compared with existing finite-sample results for linear systems and related analyses under…
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…
We present the first efficient averaging sampler that achieves asymptotically optimal randomness complexity and near-optimal sample complexity. For any $\delta < \varepsilon$ and any constant $\alpha > 0$, our sampler uses $m + O(\log (1 /…
We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an…
Score-based generative modeling, implemented through probability flow ODEs, has shown impressive results in numerous practical settings. However, most convergence guarantees rely on restrictive regularity assumptions on the target…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards…