Conservation Laws Characterize Likelihood in Diffusion Models.
Key takeaways
- Conservation laws provide a unified likelihood characterization for diffusion models.
- Data-model cross-entropy can be expressed as an integral of local information-theoretic derivatives.
- Training can be simplified to minimizing negative log-likelihood by learning marginal posteriors.
- Entropy is noise-path independent, but denoiser capacity affects performance.
Who benefits
Summary
This paper develops conservation laws for diffusion models based on generalized extrinsic information transfer (GEXIT) functions, showing that data-model cross-entropy can be precisely characterized as an integral of local information-theoretic derivatives. This unified framework explains likelihood for discrete and continuous diffusion, with implications for training by minimizing negative log-likelihood.
Why it matters
AI researchers and engineers working with generative models can gain a deeper theoretical understanding of diffusion models, potentially leading to more principled training objectives, improved likelihood estimation, and better model performance.
How to implement this in your domain
- 1Study the theoretical framework of conservation laws and GEXIT functions for diffusion models.
- 2Explore how to reformulate diffusion model training objectives to explicitly minimize negative log-likelihood based on marginal posteriors.
- 3Investigate the impact of different noise processes and denoiser capacities on model performance in light of the locality property.
- 4Apply the insights to design more efficient or robust training strategies for custom diffusion models.
- 5Benchmark new training approaches against traditional denoising objectives on relevant generative tasks.
Original post by Ziv Aharoni, Henry D. Pfister
"arXiv:2607.10067v1 Announce Type: new Abstract: While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (G…"
View on XOriginally posted by Ziv Aharoni, Henry D. Pfister on X · view source
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