Lanczos Gaussian Sampler Improves DDPM Path KL Divergence
A new paper on arXiv (2605.22723) introduces the Lanczos Gaussian sampler (LGS), a training-free method for sampling from the optimal reverse covariance in Gaussian denoising diffusion probabilistic models (DDPMs). The authors show that matching the full posterior covariance reduces path-space KL divergence from Ω(1/T) to O(1/T²), breaking a known barrier. LGS uses only covariance-vector products via Jacobian-vector products of the posterior mean, avoiding dense storage. This improves classifier guidance and other procedures that perturb the entire reverse trajectory.
Key facts
- arXiv paper 2605.22723
- Lanczos Gaussian sampler (LGS) introduced
- Path-space KL divergence reduced from Ω(1/T) to O(1/T²)
- Full posterior covariance matching breaks the Ω(1/T) barrier
- LGS is training-free and matrix-free
- Uses covariance-vector products via Jacobian-vector products
- Relevant for classifier guidance
- Avoids dense covariance storage
Entities
Institutions
- arXiv