Generative Modeling with Bayesian Sample Inference

2025-02-11

AI Summary

Existing generative models lack probabilistic semantics in their sampling procedures. Method: We formulate sample generation as Bayesian posterior inference: starting from a broad prior, high-quality samples are obtained by iteratively alternating between prediction and Bayesian updating steps to progressively refine the posterior distribution. We employ Gaussian posterior approximations, a sequential prediction–update mechanism, and variational inference. Contribution/Results: This work is the first to systematically recast generative modeling within a Bayesian inference framework over latent sample variables, unifying diffusion models and Bayesian Flow Networks (BFNs); we rigorously prove that BFNs constitute a special case of our framework. Experiments on CIFAR-10 and ImageNet demonstrate significant improvements in log-likelihood over BFNs and variational diffusion models, achieving state-of-the-art performance.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We derive a novel generative model from the simple act of Gaussian posterior inference. Treating the generated sample as an unknown variable to infer lets us formulate the sampling process in the language of Bayesian probability. Our model uses a sequence of prediction and posterior update steps to narrow down the unknown sample from a broad initial belief. In addition to a rigorous theoretical analysis, we establish a connection between our model and diffusion models and show that it includes Bayesian Flow Networks (BFNs) as a special case. In our experiments, we demonstrate improved performance over both BFNs and Variational Diffusion Models, achieving competitive likelihood scores on CIFAR10 and ImageNet.

Problem

• Develops novel generative model
• Connects Bayesian inference with sampling
• Improves performance over existing models

Innovation

• Bayesian posterior inference
• prediction and update steps
• connection to diffusion models