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.
Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling
Institut Denis Poisson, University of Orléans（德尼·泊松研究所，奥尔良大学）；University of Toulouse, IRIT/INP-ENSEEIHT, CNRS（图卢兹大学，法国国家信息与自动化研究所/国立高等电子、电子技术、计算机与机械学院，法国国家科学研究中心）
本文提出一种基于去噪正则化（RED）的图像反演贝叶斯框架，并设计了内含Langevin Monte Carlo步骤的分裂Gibbs采样算法，通过去模糊等任务验证了其有效性。
University of Montreal（蒙特利尔大学）；Microsoft Research Lab（微软研究院实验室）
Denoising Score Matching with Annealed Langevin Sampling (DSM-ALS) has recently found success in generative modeling. The approach works by first training a neural network to estimate the score of a distribution, and then using Langevin dynamics to sample from the data distribution assumed by the score network. Despite the convincing visual quality of samples, this method appears to perform worse than Generative Adversarial Networks (GANs) under the Fréchet Inception Distance, a standard metric for generative models. We show that this apparent gap vanishes when denoising the final Langevin sam…
NVIDIA（英伟达）；University of Waterloo（滑铁卢大学）；Vector Institute（矢量研究所）
Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The complexity of this denoising task is, apart from the data distribution itself, uniquely determined by the diffusion process. We argue that current SGMs employ overly simplistic diffusions, leading to unnecessarily complex denoising processes, which limit generative modeling performance. Based on connections to statistical mechanics, we propose a novel critically-…
We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (score…
Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations, motivating a more concrete route toward even higher dimension PDF estimation in future. We outline this limitation, before extending the theory to a broader family of noising distributions -- namely, the generalised normal distribution. To theoretically ground this, we relax a key assumption in (denoising) score matching theory, demonstrating that distributions whic…
Score-based constrained generative modeling via Langevin diffusions with boundary conditions
Institute for Analysis and Scientific Computing, TU Wien（维也纳技术大学分析与科学计算研究所）；Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg（查尔姆斯理工大学数学科学系）
This paper introduces an alternative approach to sampling from autoregressive models. Autoregressive models are typically sampled sequentially, according to the transition dynamics defined by the model. Instead, we propose a sampling procedure that initializes a sequence with white noise and follows a Markov chain defined by Langevin dynamics on the global log-likelihood of the sequence. This approach parallelizes the sampling process and generalizes to conditional sampling. Using an autoregressive model as a Bayesian prior, we can steer the output of a generative model using a conditional lik…
Nanyang Technological University（南洋理工大学）；Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）
The Denoising Autoencoder (DAE) enhances the flexibility of the data stream method in exploiting unlabeled samples. Nonetheless, the feasibility of DAE for data stream analytic deserves an in-depth study because it characterizes a fixed network capacity that cannot adapt to rapidly changing environments. Deep evolving denoising autoencoder (DEVDAN), is proposed in this paper. It features an open structure in the generative phase and the discriminative phase where the hidden units can be automatically added and discarded on the fly. The generative phase refines the predictive performance of the…
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie
University of Oxford（牛津大学）；Institut Universitaire de France（法国大学研究院）；Heriot-Watt University（赫瑞瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学科学研究所）
本文针对贝叶斯成像中 Plug & Play (PnP) 先验方法缺乏收敛证明的问题，提出了两种可证明收敛的算法 PnP-ULA 和 PnP-SGD，并建立了详细的收敛保证，适用于图像去模糊、修复和去噪等任务。
Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the transformed space, while preserving the topological properties of the original space, and investigate the effect of the latent space transformation on learning generative models and denoising corrupted data. The experimental results demonstrate that our generative and denoising models based on the proposed framework can provide better performance than convention…
Suitable lateral connections between encoder and decoder are shown to allow higher layers of a denoising autoencoder (dAE) to focus on invariant representations. In regular autoencoders, detailed information needs to be carried through the highest layers but lateral connections from encoder to decoder relieve this pressure. It is shown that abstract invariant features can be translated to detailed reconstructions when invariant features are allowed to modulate the strength of the lateral connection. Three dAE structures with modulated and additive lateral connections, and without lateral conne…
Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based on undecimated wavelet transform and an iterative image reconstruction algorithm. At the stage of prior learning, transformed feature images obtained by undecimated wavelet transform are stacked as an input of denoising autoencoder network (DAE). The highly redundant and multi-scale input enables the correlation of feature images at different channels, whic…
