On the Asymptotic Mean Square Error Optimality of Diffusion Models

• URL: http://arxiv.org/abs/2403.02957v2
• Date: Thu, 23 May 2024 09:39:31 GMT
• Title: On the Asymptotic Mean Square Error Optimality of Diffusion Models
• Authors: Benedikt Fesl, Benedikt Böck, Florian Strasser, Michael Baur, Michael Joham, Wolfgang Utschick,
• Abstract summary: Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean (CME) The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps.
• Score: 10.72484143420088
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets.

Related papers

• Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat [49.1574468325115]
  This paper presents explicit non-asymptotic bounds on the forward diffusion error in total variation (TV) We parametrise multi-modal data distributions in terms of the distance $R$ to their furthest modes and consider forward diffusions with additive and multiplicative noise.
  arXiv  Detail & Related papers  (2024-08-25T10:28:31Z)
• Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions [22.765095010254118]
  The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques.
  arXiv  Detail & Related papers  (2024-07-31T19:45:27Z)
• Diffusion Stochastic Optimization for Min-Max Problems [33.73046548872663]
  The optimistic gradient method is useful in addressing minimax optimization problems. Motivated by the observation that the conventional version suffers from the need for a large batch size, we introduce and analyze a new formulation termed Samevareps-generativeOGOG.
  arXiv  Detail & Related papers  (2024-01-26T01:16:59Z)
• Is Temperature Sample Efficient for Softmax Gaussian Mixture of Experts? [27.924615931679757]
  We explore the impacts of a dense-to-sparse gating mixture of experts (MoE) on the maximum likelihood estimation under the MoE. We propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function.
  arXiv  Detail & Related papers  (2024-01-25T01:09:09Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• AdjointDPM: Adjoint Sensitivity Method for Gradient Backpropagation of Diffusion Probabilistic Models [103.41269503488546]
  Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models with user-provided concepts. This paper aims to address the challenge of DPM customization when the only available supervision is a differentiable metric defined on the generated contents. We propose a novel method AdjointDPM, which first generates new samples from diffusion models by solving the corresponding probability-flow ODEs. It then uses the adjoint sensitivity method to backpropagate the gradients of the loss to the models' parameters.
  arXiv  Detail & Related papers  (2023-07-20T09:06:21Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Fast Diffusion Model [122.36693015093041]
  Diffusion models (DMs) have been adopted across diverse fields with their abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a DM optimization perspective.
  arXiv  Detail & Related papers  (2023-06-12T09:38:04Z)
• On Accelerating Diffusion-Based Sampling Process via Improved Integration Approximation [12.882586878998579]
  A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE) We consider accelerating several popular ODE-based sampling processes by optimizing certain coefficients via improved integration approximation (IIA) We show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-r than the original counterparts.
  arXiv  Detail & Related papers  (2023-04-22T06:06:28Z)
• Optimization of Annealed Importance Sampling Hyperparameters [77.34726150561087]
  Annealed Importance Sampling (AIS) is a popular algorithm used to estimates the intractable marginal likelihood of deep generative models. We present a parameteric AIS process with flexible intermediary distributions and optimize the bridging distributions to use fewer number of steps for sampling. We assess the performance of our optimized AIS for marginal likelihood estimation of deep generative models and compare it to other estimators.
  arXiv  Detail & Related papers  (2022-09-27T07:58:25Z)

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.