Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models

• URL: http://arxiv.org/abs/2309.11420v1
• Date: Wed, 20 Sep 2023 15:51:10 GMT
• Title: Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models
• Authors: Song Mei, Yuchen Wu
• Abstract summary: We investigate the approximation efficiency of score functions by deep neural networks in generative modeling. We observe score functions can often be well-approximated in graphical models through variational inference denoising algorithms. We provide an efficient sample complexity bound for diffusion-based generative modeling when the score function is learned by deep neural networks.
• Score: 22.353510613540564
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of dimensionality for intrinsically high-dimensional data. This limitation is pronounced in graphical models such as Markov random fields, common for image distributions, where the approximation efficiency of score functions remains unestablished. To address this, we observe score functions can often be well-approximated in graphical models through variational inference denoising algorithms. Furthermore, these algorithms are amenable to efficient neural network representation. We demonstrate this in examples of graphical models, including Ising models, conditional Ising models, restricted Boltzmann machines, and sparse encoding models. Combined with off-the-shelf discretization error bounds for diffusion-based sampling, we provide an efficient sample complexity bound for diffusion-based generative modeling when the score function is learned by deep neural networks.

Related papers

• Physics-informed neural networks (PINNs) for numerical model error approximation and superresolution [3.4393226199074114]
  We propose physics-informed neural networks (PINNs) for simultaneous numerical model error approximation and superresolution. PINNs effectively predict model errors in both x and y displacement fields with small differences between predictions and ground truth. Our findings demonstrate that the integration of physics-informed loss functions enables neural networks (NNs) to surpass a purely data-driven approach for approximating model errors.
  arXiv  Detail & Related papers  (2024-11-14T17:03:09Z)
• Supervised Score-Based Modeling by Gradient Boosting [49.556736252628745]
  We propose a Supervised Score-based Model (SSM) which can be viewed as a gradient boosting algorithm combining score matching. We provide a theoretical analysis of learning and sampling for SSM to balance inference time and prediction accuracy. Our model outperforms existing models in both accuracy and inference time.
  arXiv  Detail & Related papers  (2024-11-02T07:06:53Z)
• Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization [45.72323731094864]
  We present a theoretical framework to analyze two-layer neural network-based diffusion models. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.
  arXiv  Detail & Related papers  (2024-02-03T00:20:25Z)
• The Hidden Linear Structure in Score-Based Models and its Application [2.1756081703276]
  We show that for well-trained diffusion models, the learned score at a high noise scale is well approximated by the linear score of Gaussian. Our finding of the linear structure in the score-based model has implications for better model design and data pre-processing.
  arXiv  Detail & Related papers  (2023-11-17T22:25:07Z)
• Generative Neural Fields by Mixtures of Neural Implicit Functions [43.27461391283186]
  We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in a latent space by either conducting meta-learning or adopting auto-decoding paradigms.
  arXiv  Detail & Related papers  (2023-10-30T11:41:41Z)
• Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation [10.793646707711442]
  We present a framework for training generative models for density estimation. We use the score-based diffusion model to generate labeled data. Once the labeled data are generated, we can train a simple fully connected neural network to learn the generative model in the supervised manner.
  arXiv  Detail & Related papers  (2023-10-22T23:56:19Z)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Sparse Flows: Pruning Continuous-depth Models [107.98191032466544]
  We show that pruning improves generalization for neural ODEs in generative modeling. We also show that pruning finds minimal and efficient neural ODE representations with up to 98% less parameters compared to the original network, without loss of accuracy.
  arXiv  Detail & Related papers  (2021-06-24T01:40:17Z)

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.