gDDIM: Generalized denoising diffusion implicit models (2206.05564v2)

Abstract: Our goal is to extend the denoising diffusion implicit model (DDIM) to general diffusion models~(DMs) besides isotropic diffusions. Instead of constructing a non-Markov noising process as in the original DDIM, we examine the mechanism of DDIM from a numerical perspective. We discover that the DDIM can be obtained by using some specific approximations of the score when solving the corresponding stochastic differential equation. We present an interpretation of the accelerating effects of DDIM that also explains the advantages of a deterministic sampling scheme over the stochastic one for fast sampling. Building on this insight, we extend DDIM to general DMs, coined generalized DDIM (gDDIM), with a small but delicate modification in parameterizing the score network. We validate gDDIM in two non-isotropic DMs: Blurring diffusion model (BDM) and Critically-damped Langevin diffusion model (CLD). We observe more than 20 times acceleration in BDM. In the CLD, a diffusion model by augmenting the diffusion process with velocity, our algorithm achieves an FID score of 2.26, on CIFAR10, with only 50 number of score function evaluations~(NFEs) and an FID score of 2.86 with only 27 NFEs. Code is available at https://github.com/qsh-zh/gDDIM

• The paper presents gDDIM, which modifies score parameterization to extend DDIM’s applicability beyond isotropic diffusions, significantly speeding up sampling.
• The authors compare deterministic and stochastic sampling, showing that a specific numerical approach in gDDIM enhances generation speed and reliability.
• Empirical results in models like BDM and CLD demonstrate over 20× speed improvements with maintained quality, highlighting practical and theoretical benefits.

gDDIM: Generalized Denoising Diffusion Implicit Models

The paper proposes an extension to the denoising diffusion implicit model (DDIM) termed Generalized DDIM (gDDIM), aiming to accelerate the sampling process across various diffusion models (DMs). The fundamental innovation lies in a modest modification of score parameterization which allows gDDIM to be applied effectively beyond isotropic diffusion models.

Technical Insights

1. Score Approximation and Numerical Perspective: The authors embark on an analytical journey by considering DDIM through a numerical lens, discovering that certain approximations of the score, when used to solve the corresponding stochastic differential equation (SDE), reproduce the DDIM. This opens pathways to extend DDIM methodology to general DMs beyond just isotropic diffusions.
2. Deterministic vs. Stochastic Sampling: The paper explores comparing deterministic sampling schemes with stochastic ones, where deterministic sampling in DDIM is indicated to perform better by using a specific numerical method rather than the traditional Markov process. This insight is crucial, especially when generation speeds are a concern.
3. Generalization to Non-Isotropic Diffusions: The research shows the capability of gDDIM implemented in Blurring Diffusion Model (BDM) and Critically-damped Langevin Model (CLD). Remarkable accelerations were observed, indicating that gDDIM with altered score network parameterization could improve sampling speed.

Empirical Results

The validation of gDDIM was conducted on non-isotropic diffusion models, where it demonstrated significant acceleration capabilities:

• In BDM, gDDIM achieved over 20 times speed up compared to baseline samplers.
• In CLD, leveraging diffusion processes augmented with velocity, gDDIM managed quality scores (FID) on CIFAR10 dataset with minimal score function evaluations.

Implications and Future Directions

Practical Implications

The proposed gDDIM offers a robust alternative to improving the speed and efficiency of sampling processes across different diffusion models, potentially transforming applications demanding quick generation, such as real-time image synthesis or high-resolution data modalities.

Theoretical Insights

The research integrates manifold hypothesis-derived perspectives into score-based modeling, potentially paving the way for further theoretical exploration in leveraging data structures in generative models.

Conclusion

The introduction of gDDIM signifies a practical and theoretical advancement in the field of diffusion models. By extending the flexibility of DDIM across diverse diffusion processes, the paper sets a foundation for future exploration and utilization of fast sampling techniques in AI-driven generative modeling.