New paper proves sub-Gaussian errors are necessary for unbiased sampling
Gu et al. show any weaker error assumptions break tractability of sampling.
Deep Dive
Researchers Gu, Tian, Yang, and Zhu provide a tight characterization of inexact score oracle access needed for sampling with vanishing total variation bias. Their main result proves that any error weaker than the sub-Gaussian assumption rules out tractable unbiased sampling. This strengthens prior work (CCSW26) to be algorithm-agnostic and holds for a wider range of error assumptions. The paper is 5 pages and includes 1 figure.
Key Points
- Provides tight characterization of when inexact score oracles allow unbiased sampling with vanishing total variation bias.
- Proves that any error weaker than sub-Gaussian assumption rules out tractable unbiased sampling, strengthening prior CCSW26 result.
- Result is algorithm-agnostic and holds for a wide range of error assumptions, not just specific settings.
Why It Matters
Establishes fundamental limits for diffusion model training and Bayesian sampling, guiding algorithm design.