Tweedie's Formula Extended to Non-Gaussian Diffusion Models for Images and Finance
New math unlocks diffusion models for geometric Brownian motion and Cox-Ingersoll-Ross processes.
Deep Dive
The authors extend Tweedie’s formula—the backbone of denoising score matching—to three non-Gaussian processes: geometric Brownian motion (GBM), squared Bessel (BESQ), and Cox-Ingersoll-Ross (CIR). They derive new denoising objectives and demonstrate applications in image generation (using GBM and CIR) and financial time series modeling, with additional empirical Bayes estimation under the BESQ setting.
Key Points
- Extends Tweedie's formula to geometric Brownian motion (GBM), squared Bessel (BESQ), and Cox-Ingersoll-Ross (CIR) processes.
- Enables diffusion models with state-dependent noise, tested on image generation and financial time series (e.g., interest rate modeling).
- CIR-based diffusion achieves comparable image quality to Gaussian baselines with fewer sampling steps.
Why It Matters
Unlocks diffusion generative modeling for finance and physics, where non-Gaussian noise is the norm.