U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Models
U-Nets are among the most widely used architectures in computer vision, renowned for their exceptional performance in applications such as image segmentation, denoising, and diffusion modeling. However, a theoretical explanation of the U-Net architecture design has not yet been fully established. This paper introduces a novel interpretation of the U-Net architecture by studying certain generative hierarchical models, which are tree-structured graphical models extensively utilized in both language and image domains. With their encoder-decoder structure, long skip connections, and pooling and up-sampling layers, we demonstrate how U-Nets can naturally implement the belief propagation denoising algorithm in such generative hierarchical models, thereby efficiently approximating the denoising functions. This leads to an efficient sample complexity bound for learning the denoising function using U-Nets within these models. Additionally, we discuss the broader implications of these findings for diffusion models in generative hierarchical models. We also demonstrate that the conventional architecture of convolutional neural networks (ConvNets) is ideally suited for classification tasks within these models. This offers a unified view of the roles of ConvNets and U-Nets, highlighting the versatility of generative hierarchical models in modeling complex data distributions across language and image domains.
Code (0)
등록된 구현이 없습니다.
Tasks
DecoderDenoisingImage SegmentationSemantic SegmentationMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Predicting distributions with Linearizing Belief Networks
Conditional belief networks introduce stochastic binary variables in neural networks. Contrary to a classical neural network, a belief network can predict more than the expected value of the output $Y$ given the input $X…
DenoisingFacial expression generationImage Denoisingtext-to-speech+2Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes
We show how to use unlabeled data and a deep belief net (DBN) to learn a good covariance kernel for a Gaussian process. We first learn a deep generative model of the unlabeled data using the fast, greedy algorithm introd…
Gaussian ProcessesGeneral ClassificationregressionBelief Propagation as Diffusion
We introduce novel belief propagation algorithms to estimate the marginals of a high dimensional probability distribution. They involve natural (co)homological constructions relevant for a localised description of statis…
Learning in Deep Factor Graphs with Gaussian Belief Propagation
We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as …
Continual LearningDenoisingimage-classificationImage Classification+1Slice Sampling Particle Belief Propagation
Inference in continuous label Markov random fields is a challenging task. We use particle belief propagation (PBP) for solving the inference problem in continuous label space. Sampling particles from the belief distribut…
DenoisingImage Denoising