Gotta Go Fast When Generating Data with Score-Based Models (2105.14080v1)

Abstract: Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.

• The paper introduces an adaptive stochastic solver that leverages stochastic Improved Euler’s method with extrapolation to enable larger, efficient steps with only two score function evaluations per step.
• The paper employs the l2 norm for error handling, reducing the impact of high-dimensional errors and enhancing sample quality in image generation tasks.
• The paper demonstrates a 2-10x speed improvement in data generation while maintaining or improving quality metrics such as FID, alleviating the computational burden of traditional solvers.

Efficient Sampling from Score-Based Models Using Adaptive SDE Solvers

The paper "Gotta Go Fast When Generating Data with Score-Based Models" investigates a novel approach to improve the sampling efficiency of score-based generative models, specifically focusing on the optimization of the stochastic differential equation (SDE) solvers traditionally employed in these models. Score-based models, a type of denoising diffusion model, have demonstrated significant capabilities in generating high-quality, diverse datasets across various modalities, including images and audio. Despite their potential, these models are computationally intensive, largely due to the inefficiencies of the Euler-Maruyama (EM) solver, which is predominantly used for numerical integration in the reverse diffusion process.

Contributions and Methodology

The authors propose an innovative SDE solver that leverages adaptive step sizes tailored specifically to score-based generative models. This adaptive approach differentiates it from the fixed step-size EM solver, potentially offering enhanced efficiency and sample quality. The primary contributions of their work can be summarized as follows:

1. Adaptive SDE Solver: The paper introduces a custom SDE solver utilizing stochastic Improved Euler's method for integration. This method requires only two score function evaluations per step and incorporates an extrapolation technique to maintain precision while enabling larger step sizes than EM, thus improving computation speed and sample quality without the need for step size tuning.
2. Error Handling via Norms: The solver utilizes the $\ell_2$ norm instead of the $\ell_\infty$ norm for scaled error calculation, which mitigates the impact of high-dimensionality, particularly in image generation tasks. This strategic choice helps prevent local errors in individual data dimensions from disproportionately affecting global computational efficiency.
3. No Tuning Requirement: The proposed solver does not necessitate any explicit step size tuning, making it adaptable for diverse applications such as Variance Exploding (VE) and Variance Preserving (VP) processes, thereby addressing another limitation of existing approaches.

Numerical Results and Analysis

The empirical evaluation highlights that the proposed solver achieves significant improvements in both speed and sample quality when compared to the conventional EM method and other alternatives such as Probability Flow and DDIM. Key findings include:

• The adaptive solver accelerates data generation by 2 to 10 times compared to EM while maintaining or improving the sample quality, as evidenced by metrics such as the Fréchet Inception Distance (FID).
• On high-resolution datasets, the solver outperforms other methods tested, producing superior quality outputs with fewer computational resources.
• The work demonstrates that adaptive solvers can effectively traverse the trade-off between computational budget (number of score function evaluations) and output fidelity, establishing a robust framework for the efficient generation of data from score-based models.

Implications and Future Work

The paper substantially contributes to the field of generative modeling by offering a method to significantly reduce the computational overhead associated with data generation in score-based models. Although the work primarily addresses image datasets, future research could expand its applicability to other data forms, further optimizing generative tasks. Potential extensions include integrating the solver with various model architectures and evaluating its performance across different domains.

In conclusion, this paper presents a meaningful advancement in enhancing the practicality and accessibility of score-based models by proposing an efficient and adaptive approach to solving the reverse diffusion process. These developments hold promising implications, paving the way for faster and more accurate generative models while alleviating the computational burden associated with traditional SDE solvers.