Fast Sampling of Diffusion Models with Exponential Integrator
Diffusion models (DMs) have emerged as a crucial component within the field of generative modeling, achieving high-fidelity results in various tasks ranging from image generation to the resolution of inverse problems. Despite their significant accuracy and potential, DMs remain hindered by a slow sampling process—created by the need for numerous time discretization steps to achieve satisfactory sample quality. This paper addresses the challenge of accelerating the sampling phase of DMs without sacrificing result quality by carefully analyzing and optimizing the method of discretization used in the diffusion process.
Key Contributions
The paper introduces the Diffusion Exponential Integrator Sampler (DEIS) as a novel approach to fast sampling. DEIS builds on the exponential integrator, a method traditionally used for discretizing ordinary differential equations (ODEs), and applies it to the semilinear structure of the learned diffusion process found in DMs. This technique mitigates discretization error, and its numerical evaluations demonstrate an ability to produce high-quality samples with as few as 10 sampling steps. Furthermore, DEIS achieves state-of-the-art performance in scenarios with limited score function evaluations.
Key contributions of the paper include:
- Error Analysis for Fast Sampling: This paper proposes analyzing a family of marginal equivalent stochastic and ordinary differential equations (SDEs/ODEs) for fast sampling and performs a systematic error analysis for their numerical solvers.
- Development of DEIS: Introducing a sampling scheme that applies to any DMs, coupled with the Exponential Integrator, to yield superior sampling quality under limited NFE budgets. DEIS is also positioned as an asset for speeding up data log-likelihood evaluations.
- Justification of DDIM's Efficacy: The deterministic DDIM, a known sampling technique, is shown to be a specific case of DEIS, thus providing a discretization-based justification for DDIM's effectiveness.
- Empirical Validation: Comprehensive experiments on key datasets like CIFAR10 illustrate DEIS's efficiency and effectiveness, achieving notable FID scores with minimal NFEs.
Methodology Insights
The examination of discretization error unveils that different time step discretization schemes influence the quality of sample generation markedly. The researchers found that standard approaches like Euler methods are suboptimal; instead, adopting Exponential Integrators leverages the semilinear structure to tackle and minimize the associated errors. A significant discovery is that the approximation error induced by wrong discretization paths grows rapidly, particularly as time approaches zero, which mandates cautious adjustment of the step size.
Moreover, recasting the score model parameterization plays a vital role in enhancing DEIS's efficacy. The transformation to a time-dependent variable circumvents the rapid changes in score values typically occurring near the sampling's beginning and end, reducing overall approximation errors when small numbers of steps are taken.
Implications and Future Directions
This work carries substantial practical and theoretical implications. The introduction of DEIS augments the arsenal of efficient sampling techniques for DMs, emphasizing the importance of careful discretization in achieving rapid results without quality degradation. Practically, this could substantially expedite applications of diffusion models in realistic settings, unlocking new potential for real-time applications of DM-based technologies.
Looking forward, a deeper integration of these findings could be transformative for real-time generative modeling tasks, particularly in environments where computational resources or evaluation times are constrained. Additionally, exploring adaptive schemes tied to Exponential Integrator baselines and extending similar paradigms to different model structures or other machine learning domains offers fertile soil for further research.
In summary, "Fast Sampling of Diffusion Models with Exponential Integrator" delivers a profound exploration into sampling efficiency enhancements in DMs, promising applications and impactful efficiencies across the model’s lifecycle in real-world scenarios.