Finite-Sample Lens for Understanding Diffusion Posterior Sampler Failures
This paper introduces a finite-sample theoretical framework for analyzing diffusion model posterior samplers used in imaging inverse problems. The authors show that popular likelihood approximations at intermediate timesteps systematically under- or over-estimate posterior spread, leading to failure modes including sensitivity to early stopping, incorrect weighting of posterior modes, and hallucination of prior or likelihood modes. Crucially, they demonstrate these failures can arise from a multimodal prior alone, without requiring nonlinear measurement models or multimodal posteriors. The framework is model-agnostic and can serve as a diagnostic tool for evaluating existing and future posterior samplers.
Related guides (3)
Related events (8)
Exact Posterior Score (EPS): Closed-form posterior sampling for linear inverse problems with diffusion models
A new arXiv preprint derives the exact posterior score in closed form for linear Gaussian inverse problems under general Gaussian interpolants, showing that posterior sampling reduces to a denoising problem at an operator-dependent shifted pivot under anisotropic noise covariance. The authors convert this identity into a training objective called Exact Posterior Score (EPS) that preserves the input/output structure of standard diffusion pretraining, enabling training from scratch or fine-tuning from a pretrained denoiser. EPS is evaluated on five linear inverse problems across FFHQ and ImageNet, outperforming both training-free and training-based baselines while requiring roughly an order of magnitude fewer denoiser evaluations than gradient-based posterior samplers.
GADD: Gibbs-Accelerated Discrete Diffusion Achieves Polylog Sampling Complexity
This paper introduces Gibbs-Accelerated Discrete Diffusion (GADD), a corrector method for uniform-rate discrete diffusion models that constructs Gibbs posterior likelihoods directly from the concrete score function without additional training. GADD achieves O(polylog(ε⁻¹)) sampling complexity, the first such rate for diffusion-based samplers in this setting. Experiments on synthetic data, zero-shot text sampling, and zero-shot conditional music generation show consistent improvements in sample quality and wall-clock efficiency over Euler and CTMC baselines. The work also introduces a novel induction-based theoretical framework for analyzing predictor-corrector methods in discrete diffusion.
The Annotated Diffusion Model
A Hugging Face blog post providing a detailed, annotated walkthrough of diffusion models for image generation, likely covering the mathematical foundations and implementation details of denoising diffusion probabilistic models (DDPMs). The post serves as an educational deep-dive into the architecture and training process of diffusion-based generative models. Published in mid-2022, it coincides with the period of rapid growth in diffusion model adoption.
KLIP: Localized OOD Detection in Inverse Problems via KL-Divergence with Diffusion Priors
KLIP proposes an out-of-distribution detection metric for computational imaging that computes KL-divergence between a diffusion model prior and the posterior distribution. Unlike prior approaches, it requires no calibration data or knowledge of the shifted distribution, and can both flag whole images and localize OOD patches within images. The method is validated on medical imaging tasks such as detecting liver tumors in CT scans and generalizes across diffusion model architectures, datasets, and inverse problem types.
LESS: Adaptive mutual-stability sampling cuts diffusion LLM decoding steps by 72%
Researchers introduce LESS, a training-free adaptive sampler for diffusion large language models that treats token commitment as an online stopping problem. The method uses a joint stability rule combining confidence, persistence, and distributional stability to decide when to unmask tokens, avoiding wasted computation on already-stable positions. Evaluated on Dream-7B, LLaDA-8B, and LLaDA-1.5-8B across seven benchmarks, LESS reduces reverse denoising steps by 72.1% versus fixed-budget decoding while improving accuracy over prior adaptive samplers. The step reductions translate directly to fewer Transformer forward passes and lower wall-clock latency.
PTL-Diffusion: Diffusion framework with periodic terminal laws for manifold-aware generation
PTL-Diffusion is a new diffusion modeling framework that replaces the standard single Gaussian terminal distribution with a periodic family of Gaussian terminal laws, embedding phase structure directly into the forward noising dynamics rather than only in the denoising network. The authors derive closed-form forward marginals and reverse posteriors for a periodically forced Ornstein-Uhlenbeck process, enabling standard noise-prediction training. Experiments on torus, cylinder, and face datasets show improvements in manifold-level distributional matching over DDPM baselines. The work is a proof-of-concept motivating structured terminal reference laws as a direction for geometry-aware generative modeling.
Exploring Quantization Backends in Diffusers
Hugging Face published a technical overview of quantization backends available in the Diffusers library for image and video generation models. The post covers integration with multiple quantization frameworks (likely bitsandbytes, GGUF, torchao, and similar) and their trade-offs for diffusion model inference. It targets practitioners seeking to reduce memory footprint and improve throughput when deploying diffusion models.
SURGE: Approximation-free Training-Free Particle Filter for Diffusion Surrogate
The paper introduces URGE (Unbiased Resampling via Girsanov Estimation), a derivative-free inference-time scaling algorithm for diffusion models that performs path-wise importance reweighting using a Girsanov change of measure. Unlike existing inference-time guidance methods, URGE requires no score, Hessian, or PDE evaluations, attaching multiplicative weights to simulated trajectories and periodically resampling. The authors establish a theoretical equivalence between path-wise and particle-wise sequential Monte Carlo (SMC), guaranteeing unbiased terminal distributions. Empirically, URGE outperforms existing inference-time guidance baselines on synthetic tests and diffusion-model benchmarks while being simpler to implement.