Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
We establish finite-sample guarantees for conditional diffusion models learned from data and implemented with finitely many denoising steps.
ProofPaper ↗
Key points
- Under a smooth conditional density model, we derive high-probability bounds on the generated distribution's error and quantify the required number of score evaluations.
- For every smoothness index $β>0$, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence $\widetilde Op(n^{-2β/(dx+dy+2β)})$ relative to the original target with or without early stopping.
- Both the full and early-stopped samplers attain average target total-variation (TV) error $\widetilde Op(n^{-β/(dx+dy+2β)})$.
- The total-variation bound matches the rate established in existing conditional distribution-estimation theory, up to logarithmic factors.
Sources (1)
- [1]Finite-Sample Guarantees for Fully Discrete Conditional Diffusion ModelsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 9, 04:59 PM
We establish finite-sample guarantees for conditional diffusion models learned from data and implemented with finitely many denoising steps.
Under a smooth conditional density model, we derive high-probability bounds on the generated distribution's error and quantify the required number of score evaluations.
Extractive summary: sentences quoted from the sources.
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