What's the score? Automated Denoising Score Matching for Nonlinear Diffusions

• URL: http://arxiv.org/abs/2407.07998v1
• Date: Wed, 10 Jul 2024 19:02:19 GMT
• Title: What's the score? Automated Denoising Score Matching for Nonlinear Diffusions
• Authors: Raghav Singhal, Mark Goldstein, Rajesh Ranganath,
• Abstract summary: Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling. We introduce a family of tractable denoising score matching objectives, called local-DSM. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes.
• Score: 25.062104976775448
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

Related papers

• On the Relation Between Linear Diffusion and Power Iteration [42.158089783398616]
  We study the generation process as a correlation machine'' We show that low frequencies emerge earlier in the generation process, where the denoising basis vectors are more aligned to the true data with a rate depending on their eigenvalues. This model allows us to show that the linear diffusion model converges in mean to the leading eigenvector of the underlying data, similarly to the prevalent power iteration method.
  arXiv  Detail & Related papers  (2024-10-16T07:33:12Z)
• Bellman Diffusion: Generative Modeling as Learning a Linear Operator in the Distribution Space [72.52365911990935]
  We introduce Bellman Diffusion, a novel DGM framework that maintains linearity in MDPs through gradient and scalar field modeling. Our results show that Bellman Diffusion achieves accurate field estimations and is a capable image generator, converging 1.5x faster than the traditional histogram-based baseline in distributional RL tasks.
  arXiv  Detail & Related papers  (2024-10-02T17:53:23Z)
• 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)
• Local Convergence of Gradient Descent-Ascent for Training Generative Adversarial Networks [20.362912591032636]
  We study the local dynamics of gradient descent-ascent (GDA) for training a GAN with a kernel-based discriminator. We show phase transitions that indicate when the system converges, oscillates, or diverges.
  arXiv  Detail & Related papers  (2023-05-14T23:23:08Z)
• Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent [97.64313409741614]
  We propose to enforce a emphconsistency property which states that predictions of the model on its own generated data are consistent across time. We show that our novel training objective yields state-of-the-art results for conditional and unconditional generation in CIFAR-10 and baseline improvements in AFHQ and FFHQ.
  arXiv  Detail & Related papers  (2023-02-17T18:45:04Z)
• 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-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• Distilling Model Failures as Directions in Latent Space [87.30726685335098]
  We present a scalable method for automatically distilling a model's failure modes. We harness linear classifiers to identify consistent error patterns, and induce a natural representation of these failure modes as directions within the feature space. We demonstrate that this framework allows us to discover and automatically caption challenging subpopulations within the training dataset, and intervene to improve the model's performance on these subpopulations.
  arXiv  Detail & Related papers  (2022-06-29T16:35:24Z)
• Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning [78.83598532168256]
  Marginal-likelihood based model-selection is rarely used in deep learning due to estimation difficulties. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable.
  arXiv  Detail & Related papers  (2021-04-11T09:50:24Z)

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.