  We develop a framework for non-asymptotic analysis of deterministic samplers
used for diffusion generative modeling. Several recent works have analyzed
stochastic samplers using tools like Girsanov's theorem and a chain rule
variant of the interpolation argument. Unfortunately, these techniques give
vacuous bounds when applied to deterministic samplers. We give a new
operational interpretation for deterministic sampling by showing that one step
along the probability flow ODE can be expressed as two steps: 1) a restoration
step that runs gradient ascent on the conditional log-likelihood at some
infinitesimally previous time, and 2) a degradation step that runs the forward
process using noise pointing back towards the current iterate. This perspective
allows us to extend denoising diffusion implicit models to general, non-linear
forward processes. We then develop the first polynomial convergence bounds for
these samplers under mild conditions on the data distribution.
