Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective

• URL: http://arxiv.org/abs/2308.14085v1
• Date: Sun, 27 Aug 2023 12:16:33 GMT
• Title: Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective
• Authors: Davide Ghio, Yatin Dandi, Florent Krzakala and Lenka Zdeborov\'a
• Abstract summary: We focus on a class of probability distribution widely studied in the statistical physics of disordered systems. We leverage the fact that sampling via flow-based, diffusion-based or autoregressive networks methods can be equivalently mapped to the analysis of a Bayes optimal denoising of a modified probability measure. Our conclusions go both ways: we identify regions of parameters where these methods are unable to sample efficiently, while that is possible using standard Monte Carlo or Langevin approaches.
• Score: 18.278073129757466
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent years witnessed the development of powerful generative models based on flows, diffusion or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas. A theoretical analysis of the performance and understanding of the limitations of these methods remain, however, challenging. In this paper, we undertake a step in this direction by analysing the efficiency of sampling by these methods on a class of problems with a known probability distribution and comparing it with the sampling performance of more traditional methods such as the Monte Carlo Markov chain and Langevin dynamics. We focus on a class of probability distribution widely studied in the statistical physics of disordered systems that relate to spin glasses, statistical inference and constraint satisfaction problems. We leverage the fact that sampling via flow-based, diffusion-based or autoregressive networks methods can be equivalently mapped to the analysis of a Bayes optimal denoising of a modified probability measure. Our findings demonstrate that these methods encounter difficulties in sampling stemming from the presence of a first-order phase transition along the algorithm's denoising path. Our conclusions go both ways: we identify regions of parameters where these methods are unable to sample efficiently, while that is possible using standard Monte Carlo or Langevin approaches. We also identify regions where the opposite happens: standard approaches are inefficient while the discussed generative methods work well.

Related papers

• Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics [7.873510219469276]
  We introduce two novel training methods for discrete diffusion samplers. These methods yield memory-efficient training and achieve state-of-the-art results in unsupervised optimization. We introduce adaptations of SN-NIS and Neural Chain Monte Carlo that enable for the first time the application of discrete diffusion models to this problem.
  arXiv  Detail & Related papers  (2025-02-12T18:59:55Z)
• Diffusion Models for Inverse Problems in the Exponential Family [45.560812800359685]
  We extend diffusion models to handle inverse problems where the observations follow a distribution from the exponential family. We introduce the evidence trick, a method that provides a tractable approximation to the likelihood score. We demonstrate the real-world impact of our methodology by showing that it performs competitively with the current state-of-the-art in predicting malaria prevalence estimates in Sub-Saharan Africa.
  arXiv  Detail & Related papers  (2025-02-09T18:56:57Z)
• Sequential Controlled Langevin Diffusions [80.93988625183485]
  Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. We present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-
  arXiv  Detail & Related papers  (2024-12-10T00:47:10Z)
• Improved off-policy training of diffusion samplers [93.66433483772055]
  We study the problem of training diffusion models to sample from a distribution with an unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods. Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work.
  arXiv  Detail & Related papers  (2024-02-07T18:51:49Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Implicit Variational Inference for High-Dimensional Posteriors [7.924706533725115]
  In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler.
  arXiv  Detail & Related papers  (2023-10-10T14:06:56Z)
• Observation-Guided Diffusion Probabilistic Models [41.749374023639156]
  We propose a novel diffusion-based image generation method called the observation-guided diffusion probabilistic model (OGDM) Our approach reestablishes the training objective by integrating the guidance of the observation process with the Markov chain. We demonstrate the effectiveness of our training algorithm using diverse inference techniques on strong diffusion model baselines.
  arXiv  Detail & Related papers  (2023-10-06T06:29:06Z)
• Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization [87.21285093582446]
  Diffusion Generative Flow Samplers (DGFS) is a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments. Our method takes inspiration from the theory developed for generative flow networks (GFlowNets)
  arXiv  Detail & Related papers  (2023-10-04T09:39:05Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Efficient Multimodal Sampling via Tempered Distribution Flow [11.36635610546803]
  We develop a new type of transport-based sampling method called TemperFlow. Various experiments demonstrate the superior performance of this novel sampler compared to traditional methods. We show its applications in modern deep learning tasks such as image generation.
  arXiv  Detail & Related papers  (2023-04-08T06:40:06Z)
• Pathwise Conditioning of Gaussian Processes [72.61885354624604]
  Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations. This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector. We show how this pathwise interpretation of conditioning gives rise to a general family of approximations that lend themselves to efficiently sampling Gaussian process posteriors.
  arXiv  Detail & Related papers  (2020-11-08T17:09:37Z)

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.