Generative Modeling with Bayesian Sample Inference
Marten Lienen, Marcel Kollovieh, Stephan G\"unnemann
TL;DR
This paper introduces a new generative modeling approach based on Bayesian sample inference, which iteratively refines samples through prediction and posterior updates, connecting to diffusion models and improving image sample quality.
Contribution
It presents a novel Bayesian inference-based generative model that unifies and extends diffusion models and Bayesian Flow Networks, with improved sample quality.
Findings
Enhanced sample quality on ImageNet32
Achieved comparable log-likelihoods on ImageNet32 and ImageNet64
Established theoretical connections to diffusion models
Abstract
We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a sequence of prediction and posterior update steps to iteratively narrow down the unknown sample starting 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 that our model improves sample quality on ImageNet32 over both BFNs and the closely related Variational Diffusion Models, while achieving equivalent log-likelihoods on ImageNet32 and ImageNet64. Find our code at https://github.com/martenlienen/bsi.
Peer Reviews
Decision·Submitted to ICLR 2026
The paper provides a novel perspective on generative modeling that frames sample generation as iterative Bayesian inference. • The proposed BSI framework is quite general, and the paper shows that BSI includes BFN (“Bayesian Flow Networks”) as a special case. • The includes a succinct and easy to understand comparison between the BSI and BFN / VDM frameworks.
• The proposed BSI only leads to minor improvements over the BFN and VDM models. In fact, the loglikelihood BPD metric is nearly identical compared to the BFN and VDM models on both the ImageNet 32x32 and CIFAR-10 datasets. • The paper only considers a small set of baselines – BFN and VDM – on ImageNet 32x32 and CIFAR-10. The paper should also compare to state of the art models such as “Improved Denoising Diffusion Probabilistic Models, arXiv 2025”, “Neural Diffusion Models, arXiv 2024”. • The p
- Clear probabilistic formulation with closed-form update and a principled ELBO; continuous-limit bound is neat and intuitive. - Concrete connection to VDM/BFN; proof that BFN is a limit case and discussion of Markov vs. non-Markov forward processes add theoretical clarity. - Variance reduction via log-uniform sampling is motivated analytically and validated empirically. - Competitive or better results on ImageNet32 (lower FID at matched likelihoods) and matched BPD on CIFAR-10 with controlle
- Empirical scope is narrow: small-resolution datasets (ImageNet32, CIFAR-10); no high-res, text-conditioned, or scaling-law study to substantiate broader quality claims. - The theoretical comparison to VDM emphasizes simplicity of the BSI/BFN update, but practical stability/accuracy trade-offs vs. VDM’s log-space parameterization are not quantified.
* **Novelty:** The primary strength of the paper is its novel framing of generative modeling. Viewing sample generation as the process of inferring a fixed but unknown variable via iterative posterior updates is a conceptually clean and powerful idea. This Bayesian perspective is a welcome contribution, offering a different way to think about the gradual refinement process that characterizes modern generative models. * **Theoretical Soundness:** The paper provides a rigorous theoretical fou
Despite its elegant formulation and promising results I still have doubts on the methodology and experimental validation, which raise several critical questions that weaken its overall contribution. The claims of novelty and superiority feel overstated upon closer inspection of the underlying algorithm and the lack of crucial ablation studies. 1. **Conflation of Re-framing with Algorithmic Novelty:** The core training algorithm (Algorithm 2) is structurally almost identical to standard denoisi
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Taxonomy
TopicsBayesian Methods and Mixture Models
MethodsDiffusion