Small forward-marginal score error does not guarantee stable diffusion sampling because rare numerical trajectories can enter poorly controlled regions and trigger superlinear amplification.
Contractive Diffusion Probabilistic Models
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed score matching, we propose a new criterion -- the contraction property of backward sampling in the design of DPMs, leading to a novel class of contractive DPMs (CDPMs). Our key insight is that, the contraction property can provably narrow score matching errors and discretization errors, thus our proposed CDPMs are robust to both sources of error. For practical use, we show that CDPM can leverage weights of pretrained DPMs by a simple transformation, and does not need retraining. We corroborated our approach by experiments on synthetic 1-dim examples, Swiss Roll, MNIST, CIFAR-10 32$\times$32 and AFHQ 64$\times$64 dataset. Notably, CDPM steadily improves the performance of baseline score-based diffusion models.
representative citing papers
Introduces a sequential forward-backward diffusion framework that generates adapted time series by conditioning on prior history, with a parallelizable score-matching objective and statistical guarantees for ReLU networks.
citing papers explorer
-
Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
Small forward-marginal score error does not guarantee stable diffusion sampling because rare numerical trajectories can enter poorly controlled regions and trigger superlinear amplification.
-
Diffusion Models for Adaptive Sequential Data Generation
Introduces a sequential forward-backward diffusion framework that generates adapted time series by conditioning on prior history, with a parallelizable score-matching objective and statistical guarantees for ReLU networks.
- The Ensemble Schr{\"o}dinger Bridge filter for Nonlinear Data Assimilation