arXiv:2607.10067 2026 Sampling 2 ideas extracted · analyzed Aug 30, 2026
The paper provides a path-independent likelihood identity for diffusion: endpoint conditional entropy or cross-entropy is recovered by integrating a local information-loss derivative along a sufficiently regular memoryless noise path. Its strongest transferable feature is locality: the derivative can be estimated from marginal denoiser posteriors at each noise level, without evaluating a full joint reverse trajectory. This supports information-balanced diffusion schedules and likelihood-calibrated timestep weighting. Both ideas are directly testable with existing discrete or Gaussian diffusion implementations.
Replace uniformly spaced diffusion timesteps with a grid whose intervals contribute equal area under the local information-loss curve. The sampler then takes smaller steps in noise regions where the denoiser contributes most to likelihood and larger steps in low-information regions.
Use the conservation-law density to weight diffusion training examples by noise level instead of relying on uniform, cosine, or manually selected SNR weighting. This emphasizes noise regions whose local information contribution is largest while clipping the weights to prevent rare regions from destabilizing optimization.