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Generative Modeling with Denoising Auto-Encoders and Langevin Sampling
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abstract
We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show that both DAE and DSM provide estimates of the score of the Gaussian smoothed population density, allowing us to apply the machinery of Empirical Processes. We overcome the challenge of relying only on $L^2$ bounds on the score estimation error and provide finite-sample bounds in the Wasserstein distance between the law of the population distribution and the law of this sampling scheme. We then apply our results to the homotopy method of arXiv:1907.05600 and provide theoretical justification for its empirical success.
Forward citations
Cited by 8 Pith papers
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Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity
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Structured drift design for denoising diffusion models
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Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
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Optimization-Free Diffusion Model -- A Perturbation Theory Approach
Score estimation in diffusion models is reformulated as solving linear systems in an eigenbasis of a backward Kolmogorov operator, avoiding neural network training and forward SDE simulation.
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Discrete State Diffusion Models: A Sample Complexity Perspective
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