A.1 Proof of Proposition 4.1 Proposition 4.1 For any bounded measurable function τ(t): [0, T ] R, the following Reverse SDEs [ (1 + τ Eq. (20) is a reverse-time SDE running[ from T to 0, thus (there)are two additional minus ] signs in Eq. (21) before term A.2 Two Reparameterizations and Exact Solution under Exponential Integrator In this subsection, we will show the exact solution of SDE in both data prediction reparameterization and noise prediction reparameterization. The noise term in data prediction has smaller variance than noise prediction ones, implying the necessity of adopting data prediction reparameterization for the SDE sampler. The computation of variance uses the Itô Isometry, which is a crucial fact of Itô integral. Similar with Proposition 4.2, Eq. (37) can be solved analytically, which is shown in the following propositon: Following the derivation in Proposition 4.2, the mean of the Itô integral term is: [ A.2.4 Comparison between Data and Noise Reparameterizations In Table 1 we perform an ablation study on data and noise reparameterizations, the experiment results show that under the same magnitude of stochasticity, the proposed SA-Solver in data reparameterization has a better convergence which leads to better FID results under the same NFEs. In this subsection, we provide a theoretical view of this phenomenon.

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed.

SEEDS outperform or are competitive with previous SDE solvers.

Code is available at https://github.com/wl-zhao/UniPC . In this paper, we propose a training-free framework for the fast sampling of DPMs called UniPC .

One approach for tackling this problem is rectified flows, which iteratively learn smooth ODE paths that are less susceptible to truncation error. However, rectified flows still require a relatively large number of function evaluations (NFEs). In this work, we propose improved techniques for training rectified flows, allowing them to compete with knowledge distillation methods even in the low NFE setting.

H . (32) We refer to ( H

As outlined in Sec. 3, thep-th TTM is simply thep-th order Taylor polynomialapplied to an ODE.

Denoising diffusion models (DDMs) have emerged as a powerful class of generativemodels.

Neural Information Processing Systems http://nips.cc/

The synergistic combination of hypersolvers and Neural ODEs allows for cheap inference and unlocks a newfrontierforpractical application ofcontinuous-depth models.