Optimizing Noise Schedules of Generative Models in High Dimensionss

• URL: http://arxiv.org/abs/2501.00988v1
• Date: Thu, 02 Jan 2025 00:39:00 GMT
• Title: Optimizing Noise Schedules of Generative Models in High Dimensionss
• Authors: Santiago Aranguri, Giulio Biroli, Marc Mezard, Eric Vanden-Eijnden,
• Abstract summary: We show that noise schedules specific to preserving variance (VP) and variance exploding (VE) allow for the recovery of both high- and low-level features. We also show that these schedules yield generative models for the GM and Curie-Weiss (CW) model whose probability flow ODE can be discretized.
• Score: 18.19470017419402
• License:
• Abstract: Recent works have shown that diffusion models can undergo phase transitions, the resolution of which is needed for accurately generating samples. This has motivated the use of different noise schedules, the two most common choices being referred to as variance preserving (VP) and variance exploding (VE). Here we revisit these schedules within the framework of stochastic interpolants. Using the Gaussian Mixture (GM) and Curie-Weiss (CW) data distributions as test case models, we first investigate the effect of the variance of the initial noise distribution and show that VP recovers the low-level feature (the distribution of each mode) but misses the high-level feature (the asymmetry between modes), whereas VE performs oppositely. We also show that this dichotomy, which happens when denoising by a constant amount in each step, can be avoided by using noise schedules specific to VP and VE that allow for the recovery of both high- and low-level features. Finally we show that these schedules yield generative models for the GM and CW model whose probability flow ODE can be discretized using $\Theta_d(1)$ steps in dimension $d$ instead of the $\Theta_d(\sqrt{d})$ steps required by constant denoising.

Related papers

• Distributional Diffusion Models with Scoring Rules [83.38210785728994]
  Diffusion models generate high-quality synthetic data. generating high-quality outputs requires many discretization steps. We propose to accomplish sample generation by learning the posterior em distribution of clean data samples.
  arXiv  Detail & Related papers  (2025-02-04T16:59:03Z)
• A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models [45.60426164657739]
  We develop non-asymptotic convergence theory for a diffusion-based sampler. We prove that $d/varepsilon$ are sufficient to approximate the target distribution to within $varepsilon$ total-variation distance. Our results also characterize how $ell$ score estimation errors affect the quality of the data generation processes.
  arXiv  Detail & Related papers  (2024-08-05T09:02:24Z)
• Score-based Generative Models with Adaptive Momentum [40.84399531998246]
  We propose an adaptive momentum sampling method to accelerate the transforming process. We show that our method can produce more faithful images/graphs in small sampling steps with 2 to 5 times speed up.
  arXiv  Detail & Related papers  (2024-05-22T15:20:27Z)
• 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)
• Doubly Stochastic Models: Learning with Unbiased Label Noises and Inference Stability [85.1044381834036]
  We investigate the implicit regularization effects of label noises under mini-batch sampling settings of gradient descent. We find such implicit regularizer would favor some convergence points that could stabilize model outputs against perturbation of parameters. Our work doesn't assume SGD as an Ornstein-Uhlenbeck like process and achieve a more general result with convergence of approximation proved.
  arXiv  Detail & Related papers  (2023-04-01T14:09:07Z)
• Denoising Diffusion Samplers [41.796349001299156]
  Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. We explore a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling.
  arXiv  Detail & Related papers  (2023-02-27T14:37:16Z)
• Subspace Diffusion Generative Models [4.310834990284412]
  Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We restrict the diffusion via projections onto subspaces as the data distribution evolves toward noise. Our framework is fully compatible with continuous-time diffusion and retains its flexible capabilities.
  arXiv  Detail & Related papers  (2022-05-03T13:43:47Z)
• Score-Based Generative Modeling through Stochastic Differential Equations [114.39209003111723]
  We present a differential equation that transforms a complex data distribution to a known prior distribution by injecting noise. A corresponding reverse-time SDE transforms the prior distribution back into the data distribution by slowly removing the noise. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks. We demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
  arXiv  Detail & Related papers  (2020-11-26T19:39:10Z)

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.