Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian
Authors: Wenpin Tang, Nizar Touzi, Zikun Zhang et al.
Summary
arXiv:2605. 19391v1 Announce Type: new Abstract: Diffusion models have achieved remarkable success in generating samples from unknown data distributions.
Relevance
Read next because Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "The marker is a representational handle, not a behavioural one — sharing it between a villain persona and the assistant transfers no misalignment (HIGH confidence)", experiment "#351 follow-up: broader-vocab position-0 sweep at T=1.0 + position-1 suffix isolation". Matching terms: under, rate, model. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.19391v1 Announce Type: new Abstract: Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models.