Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models

• URL: http://arxiv.org/abs/2311.11003v1
• Date: Sat, 18 Nov 2023 07:53:22 GMT
• Title: Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models
• Authors: Xuefeng Gao, Hoang M. Nguyen, Lingjiong Zhu
• Abstract summary: Score-based generative models (SGMs) are a recent class of deep generative models with state-of-the-art performance in many applications. We establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10.
• Score: 9.47767039367222
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. We specialize our result to several concrete SGMs with specific choices of forward processes modelled by stochastic differential equations, and obtain an upper bound on the iteration complexity for each model, which demonstrates the impacts of different choices of the forward processes. We also provide a lower bound when the data distribution is Gaussian. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10. We find that the experimental results are in good agreement with our theoretical predictions on the iteration complexity, and the models with our newly proposed forward processes can outperform existing models.

Related papers

• Fusion of Gaussian Processes Predictions with Monte Carlo Sampling [61.31380086717422]
  In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes.
  arXiv  Detail & Related papers  (2024-03-03T04:21:21Z)
• Mixtures of Gaussian process experts based on kernel stick-breaking processes [0.6396288020763143]
  We propose a new mixture model of Gaussian process experts based on kernel stick-breaking processes. Our model maintains the intuitive appeal yet improve the performance of the existing models. The model behaviour and improved predictive performance are demonstrated in experiments using six datasets.
  arXiv  Detail & Related papers  (2023-04-26T21:23:01Z)
• A Complete Recipe for Diffusion Generative Models [18.891215475887314]
  We present a complete recipe for formulating forward processes in Generative Models (SGMs) We introduce Phase Space Langevin Diffusion (PSLD), which relies on score-based modeling within an augmented space enriched by auxiliary variables.
  arXiv  Detail & Related papers  (2023-03-03T07:20:58Z)
• Model ensemble instead of prompt fusion: a sample-specific knowledge transfer method for few-shot prompt tuning [85.55727213502402]
  We focus on improving the few-shot performance of prompt tuning by transferring knowledge from soft prompts of source tasks. We propose Sample-specific Ensemble of Source Models (SESoM) SESoM learns to adjust the contribution of each source model for each target sample separately when ensembling source model outputs.
  arXiv  Detail & Related papers  (2022-10-23T01:33:16Z)
• Deep Generative Modeling on Limited Data with Regularization by Nontransferable Pre-trained Models [32.52492468276371]
  We propose regularized deep generative model (Reg-DGM) to reduce the variance of generative modeling with limited data. Reg-DGM uses a pre-trained model to optimize a weighted sum of a certain divergence and the expectation of an energy function. Empirically, with various pre-trained feature extractors and a data-dependent energy function, Reg-DGM consistently improves the generation performance of strong DGMs with limited data.
  arXiv  Detail & Related papers  (2022-08-30T10:28:50Z)
• Convergence for score-based generative modeling with polynomial complexity [9.953088581242845]
  We prove the first convergence guarantees for the core mechanic behind Score-based generative modeling. Compared to previous works, we do not incur error that grows exponentially in time or that suffers from a curse of dimensionality. We show that a predictor-corrector gives better convergence than using either portion alone.
  arXiv  Detail & Related papers  (2022-06-13T14:57:35Z)
• Riemannian Score-Based Generative Modeling [56.20669989459281]
  We introduce score-based generative models (SGMs) demonstrating remarkable empirical performance. Current SGMs make the underlying assumption that the data is supported on a Euclidean manifold with flat geometry. This prevents the use of these models for applications in robotics, geoscience or protein modeling.
  arXiv  Detail & Related papers  (2022-02-06T11:57:39Z)
• Score-based Generative Modeling in Latent Space [93.8985523558869]
  Score-based generative models (SGMs) have recently demonstrated impressive results in terms of both sample quality and distribution coverage. Here, we propose the Latent Score-based Generative Model (LSGM), a novel approach that trains SGMs in a latent space. Moving from data to latent space allows us to train more expressive generative models, apply SGMs to non-continuous data, and learn smoother SGMs in a smaller space.
  arXiv  Detail & Related papers  (2021-06-10T17:26:35Z)
• Continual Learning with Fully Probabilistic Models [70.3497683558609]
  We present an approach for continual learning based on fully probabilistic (or generative) models of machine learning. We propose a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. We show that GMR achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.
  arXiv  Detail & Related papers  (2021-04-19T12:26:26Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Gaussian Process Regression with Local Explanation [28.90948136731314]
  We propose GPR with local explanation, which reveals the feature contributions to the prediction of each sample. In the proposed model, both the prediction and explanation for each sample are performed using an easy-to-interpret locally linear model. For a new test sample, the proposed model can predict the values of its target variable and weight vector, as well as their uncertainties.
  arXiv  Detail & Related papers  (2020-07-03T13:22:24Z)

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.