Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel

• URL: http://arxiv.org/abs/2406.00924v2
• Date: Thu, 17 Oct 2024 03:54:52 GMT
• Title: Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel
• Authors: Shivam Gupta, Linda Cai, Sitan Chen,
• Abstract summary: We show that our algorithm can be parallelized to run in only $widetilde O(log2 d)$ parallel rounds. We also show that our algorithm can be parallelized to run in only $widetilde O(log2 d)$ parallel rounds.
• Score: 10.840582511203024
• License:
• Abstract: Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes for diffusion sampling with provable guarantees; these works show that for essentially any data distribution, one can approximately sample in polynomial time given a sufficiently accurate estimate of its score functions at different noise levels. In this work, we propose a new scheme inspired by Shen and Lee's randomized midpoint method for log-concave sampling~\cite{ShenL19}. We prove that this approach achieves the best known dimension dependence for sampling from arbitrary smooth distributions in total variation distance ($\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work). We also show that our algorithm can be parallelized to run in only $\widetilde O(\log^2 d)$ parallel rounds, constituting the first provable guarantees for parallel sampling with diffusion models. As a byproduct of our methods, for the well-studied problem of log-concave sampling in total variation distance, we give an algorithm and simple analysis achieving dimension dependence $\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work.

Related papers

• Efficiently learning and sampling multimodal distributions with data-based initialization [20.575122468674536]
  We consider the problem of sampling a multimodal distribution with a Markov chain given a small number of samples from the stationary measure. We show that if the Markov chain has a $k$th order spectral gap, samples from the stationary distribution will efficiently generate a sample whose conditional law is $varepsilon$-close in TV distance to the stationary measure.
  arXiv  Detail & Related papers  (2024-11-14T01:37:02Z)
• Faster Sampling via Stochastic Gradient Proximal Sampler [28.422547264326468]
  Proximal samplers (SPS) for sampling from non-log-concave distributions are studied. We show that the convergence to the target distribution can be guaranteed as long as the algorithm trajectory is bounded. We provide two implementable variants based on Langevin dynamics (SGLD) and Langevin-MALA, giving rise to SPS-SGLD and SPS-MALA.
  arXiv  Detail & Related papers  (2024-05-27T00:53:18Z)
• Fast parallel sampling under isoperimetry [10.619901778151336]
  We show how to sample in parallel from a distribution $pi$ over $mathbb Rd$ that satisfies a log-Sobolev inequality. We show that our algorithm outputs samples from a distribution $hatpi$ that is close to $pi$ in Kullback--Leibler divergence.
  arXiv  Detail & Related papers  (2024-01-17T07:24:18Z)
• Improved Active Learning via Dependent Leverage Score Sampling [8.400581768343804]
  We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting. We propose an easily implemented method based on the emphpivotal sampling algorithm In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to $50%$.
  arXiv  Detail & Related papers  (2023-10-08T01:51:30Z)
• Stochastic Approximation Approaches to Group Distributionally Robust Optimization and Beyond [89.72693227960274]
  This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. To reduce the number of samples in each round from $m$ to 1, we cast GDRO as a two-player game, where one player conducts and the other executes an online algorithm for non-oblivious multi-armed bandits. In the second scenario, we propose to optimize the average top-$k$ risk instead of the maximum risk, thereby mitigating the impact of distributions.
  arXiv  Detail & Related papers  (2023-02-18T09:24:15Z)
• Perfect Sampling from Pairwise Comparisons [26.396901523831534]
  We study how to efficiently obtain perfect samples from a discrete distribution $mathcalD$ given access only to pairwise comparisons of elements of its support. We design a Markov chain whose stationary distribution coincides with $mathcalD$ and give an algorithm to obtain exact samples using the technique of Coupling from the Past.
  arXiv  Detail & Related papers  (2022-11-23T11:20:30Z)
• Adaptive Sketches for Robust Regression with Importance Sampling [64.75899469557272]
  We introduce data structures for solving robust regression through gradient descent (SGD) Our algorithm effectively runs $T$ steps of SGD with importance sampling while using sublinear space and just making a single pass over the data.
  arXiv  Detail & Related papers  (2022-07-16T03:09:30Z)
• Optimal Testing of Discrete Distributions with High Probability [49.19942805582874]
  We study the problem of testing discrete distributions with a focus on the high probability regime. We provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors.
  arXiv  Detail & Related papers  (2020-09-14T16:09:17Z)
• Stochastic Saddle-Point Optimization for Wasserstein Barycenters [69.68068088508505]
  We consider the populationimation barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. We employ the structure of the problem and obtain a convex-concave saddle-point reformulation of this problem. In the setting when the distribution of random probability measures is discrete, we propose an optimization algorithm and estimate its complexity.
  arXiv  Detail & Related papers  (2020-06-11T19:40:38Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)
• Non-Adaptive Adaptive Sampling on Turnstile Streams [57.619901304728366]
  We give the first relative-error algorithms for column subset selection, subspace approximation, projective clustering, and volume on turnstile streams that use space sublinear in $n$. Our adaptive sampling procedure has a number of applications to various data summarization problems that either improve state-of-the-art or have only been previously studied in the more relaxed row-arrival model.
  arXiv  Detail & Related papers  (2020-04-23T05:00:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.