Generative Modeling with Denoising Auto-Encoders and Langevin Sampling

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.Comment: 22 page

Diffusion Models in Vision: A Survey

Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward diffusion stage and a reverse diffusion stage. In the forward diffusion stage, the input data is gradually perturbed over several steps by adding Gaussian noise. In the reverse stage, a model is tasked at recovering the original input data by learning to gradually reverse the diffusion process, step by step. Diffusion models are widely appreciated for the quality and diversity of the generated samples, despite their known computational burdens, i.e. low speeds due to the high number of steps involved during sampling. In this survey, we provide a comprehensive review of articles on denoising diffusion models applied in vision, comprising both theoretical and practical contributions in the field. First, we identify and present three generic diffusion modeling frameworks, which are based on denoising diffusion probabilistic models, noise conditioned score networks, and stochastic differential equations. We further discuss the relations between diffusion models and other deep generative models, including variational auto-encoders, generative adversarial networks, energy-based models, autoregressive models and normalizing flows. Then, we introduce a multi-perspective categorization of diffusion models applied in computer vision. Finally, we illustrate the current limitations of diffusion models and envision some interesting directions for future research.Comment: Accepted in IEEE Transactions on Pattern Analysis and Machine Intelligence. 25 pages, 3 figure

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning

A Survey on Generative Diffusion Model

Deep learning shows excellent potential in generation tasks thanks to deep latent representation. Generative models are classes of models that can generate observations randomly concerning certain implied parameters. Recently, the diffusion Model has become a rising class of generative models by its power-generating ability. Nowadays, great achievements have been reached. More applications except for computer vision, speech generation, bioinformatics, and natural language processing are to be explored in this field. However, the diffusion model has its genuine drawback of a slow generation process, single data types, low likelihood, and the inability for dimension reduction. They are leading to many enhanced works. This survey makes a summary of the field of the diffusion model. We first state the main problem with two landmark works -- DDPM and DSM, and a unified landmark work -- Score SDE. Then, we present improved techniques for existing problems in the diffusion-based model field, including speed-up improvement For model speed-up improvement, data structure diversification, likelihood optimization, and dimension reduction. Regarding existing models, we also provide a benchmark of FID score, IS, and NLL according to specific NFE. Moreover, applications with diffusion models are introduced including computer vision, sequence modeling, audio, and AI for science. Finally, there is a summarization of this field together with limitations \& further directions. The summation of existing well-classified methods is in our Github:https://github.com/chq1155/A-Survey-on-Generative-Diffusion-Model

A Survey on Bayesian Deep Learning

A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty. The past decade has seen major advances in many perception tasks such as visual object recognition and speech recognition using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. In recent years, Bayesian deep learning has emerged as a unified probabilistic framework to tightly integrate deep learning and Bayesian models. In this general framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in turn, the feedback from the inference process is able to enhance the perception of text or images. This survey provides a comprehensive introduction to Bayesian deep learning and reviews its recent applications on recommender systems, topic models, control, etc. Besides, we also discuss the relationship and differences between Bayesian deep learning and other related topics such as Bayesian treatment of neural networks.Comment: To appear in ACM Computing Surveys (CSUR) 202

Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameterized energy function. The energy function is then modified so the model and data distributions match, with no guarantee on the number of steps required for the Markov chain to converge. Moreover, the detailed balance condition is highly restrictive: energy based models corresponding to neural networks must have symmetric weights, unlike biological neural circuits. In contrast, we develop a method for directly learning arbitrarily parameterized transition operators capable of expressing non-equilibrium stationary distributions that violate detailed balance, thereby enabling us to learn more biologically plausible asymmetric neural networks and more general non-energy based dynamical systems. The proposed training objective, which we derive via principled variational methods, encourages the transition operator to "walk back" in multi-step trajectories that start at data-points, as quickly as possible back to the original data points. We present a series of experimental results illustrating the soundness of the proposed approach, Variational Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating superior samples compared to earlier attempts to learn a transition operator. We also show that although each rapid training trajectory is limited to a finite but variable number of steps, our transition operator continues to generate good samples well past the length of such trajectories, thereby demonstrating the match of its non-equilibrium stationary distribution to the data distribution. Source Code: http://github.com/anirudh9119/walkback_nips17Comment: To appear at NIPS 201

Exploring Generative Neural Temporal Point Process

Temporal point process (TPP) is commonly used to model the asynchronous event sequence featuring occurrence timestamps and revealed by probabilistic models conditioned on historical impacts. While lots of previous works have focused on `goodness-of-fit' of TPP models by maximizing the likelihood, their predictive performance is unsatisfactory, which means the timestamps generated by models are far apart from true observations. Recently, deep generative models such as denoising diffusion and score matching models have achieved great progress in image generating tasks by demonstrating their capability of generating samples of high quality. However, there are no complete and unified works exploring and studying the potential of generative models in the context of event occurence modeling for TPP. In this work, we try to fill the gap by designing a unified \textbf{g}enerative framework for \textbf{n}eural \textbf{t}emporal \textbf{p}oint \textbf{p}rocess (\textsc{GNTPP}) model to explore their feasibility and effectiveness, and further improve models' predictive performance. Besides, in terms of measuring the historical impacts, we revise the attentive models which summarize influence from historical events with an adaptive reweighting term considering events' type relation and time intervals. Extensive experiments have been conducted to illustrate the improved predictive capability of \textsc{GNTPP} with a line of generative probabilistic decoders, and performance gain from the revised attention. To the best of our knowledge, this is the first work that adapts generative models in a complete unified framework and studies their effectiveness in the context of TPP. Our codebase including all the methods given in Section.5.1.1 is open in \url{https://github.com/BIRD-TAO/GNTPP}. We hope the code framework can facilitate future research in Neural TPPs