Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations (2412.08292v1)

Abstract: In diffusion models, samples are generated through an iterative refinement process, requiring hundreds of sequential model evaluations. Several recent methods have introduced approximations (fewer discretization steps or distillation) to trade off speed at the cost of sample quality. In contrast, we introduce Self-Refining Diffusion Samplers (SRDS) that retain sample quality and can improve latency at the cost of additional parallel compute. We take inspiration from the Parareal algorithm, a popular numerical method for parallel-in-time integration of differential equations. In SRDS, a quick but rough estimate of a sample is first created and then iteratively refined in parallel through Parareal iterations. SRDS is not only guaranteed to accurately solve the ODE and converge to the serial solution but also benefits from parallelization across the diffusion trajectory, enabling batched inference and pipelining. As we demonstrate for pre-trained diffusion models, the early convergence of this refinement procedure drastically reduces the number of steps required to produce a sample, speeding up generation for instance by up to 1.7x on a 25-step StableDiffusion-v2 benchmark and up to 4.3x on longer trajectories.

• The paper introduces Self-Refining Diffusion Samplers (SRDS), an algorithm that accelerates diffusion model sampling by leveraging parallel computation via Parareal iterations.
• SRDS uses a two-phase process: generating a coarse trajectory estimate and then refining it in parallel blocks, achieving up to a 4.3x speed increase while maintaining sample quality.
• This method has practical implications for enabling real-time diffusion model applications and suggests future research into integrating other parallel-in-time methods with generative models.

Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations

The paper introduces Self-Refining Diffusion Samplers (SRDS), an algorithm designed to enhance the sampling speed of diffusion models while maintaining sample quality. In contrast to many existing methods that achieve faster sample generation at the expense of quality, SRDS exploits parallel computation to refine coarse estimates iteratively, ensuring both speed and accuracy. This is accomplished through Parareal iterations, a parallel-in-time integration method traditionally applied to differential equations. The proposed approach represents a significant advancement in the field, particularly in enhancing the efficiency of generative diffusion models without sacrificing their output quality.

Methodological Innovations

SRDS makes use of a two-phase sampling process:

1. Coarse Solution: Initially, a rough estimate of the diffusion trajectory is generated via fewer steps of a standard solver, such as the DDIM or Euler solvers. This serves as a preliminary solution that is computationally inexpensive to generate.
2. Parallel Refinement: The Parareal algorithm drives the iterative refinement of these coarse solutions. This process harnesses fine solvers for precise solutions and coarse solvers for fast predictions. By partitioning the solution space into blocks, SRDS performs high-resolution simulations in parallel across these segments, progressively improving the solution's fidelity through a predictor-corrector scheme typical of Parareal methods.

Key Results and Performance Metrics

SRDS demonstrates impressive performance improvements across various benchmarks. In particular, the method achieves a 1.7x improvement in sampling speed on the 25-step StableDiffusion-v2 benchmark and up to a 4.3x increase on longer trajectories. Importantly, SRDS produces samples of high quality equivalent to sequential sampling baselines, with the fidelity of outputs being measured rigorously using metrics such as the FID score.

The algorithm's efficiency arises from its ability to produce significant speedups in sample generation while leveraging extensive batched computation and pipelined parallelization. This dual advantage of reduced latency and maintained sample quality positions SRDS as a highly versatile solution for various applications that require rapid sample generation.

Implications and Future Directions

The introduction of SRDS has both practical and theoretical implications. Practically, it opens avenues for real-time use cases of diffusion models, such as interactive applications in image and audio processing, and robotics path planning. Theoretically, the deployment of Parareal iterations within generative models can inspire further exploration into other parallel-in-time methodologies that may yield similar efficiencies.

Future research could focus on refining the underlying solver mechanisms used within SRDS to further decrease the number of required iterations for convergence. Additionally, exploring alternative parallel-in-time methods and solvers that could integrate with SRDS might unlock additional performance gains, especially in scenarios with longer diffusion trajectories.

The development of SRDS thus represents a significant stride in balancing computational efficiency with output quality in diffusion models, setting a new standard for future advancements in the domain.