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We develop a framework for non-asymptotic analysis of deterministic samplersused for diffusion generative modeling. Several recent works have analyzedstochastic samplers using tools like Girsanov's theorem and a chain rulevariant of the interpolation argument. Unfortunately, these techniques givevacuous bounds when applied to deterministic samplers. We give a newoperational interpretation for deterministic sampling by showing that one stepalong the probability flow ODE can be expressed as two steps: 1) a restorationstep that runs gradient ascent on the conditional log-likelihood at someinfinitesimally previous time, and 2) a degradation step that runs the forwardprocess using noise pointing back towards the current iterate. This perspectiveallows us to extend denoising diffusion implicit models to general, non-linearforward processes. We then develop the first polynomial convergence bounds forthese samplers under mild conditions on the data distribution.

Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers