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RBF-Solver: A Multistep Sampler for Diffusion Probabilistic Models via Radial Basis Functions

arXiv:2603.13330v1 Announce Type: new Abstract: Diffusion probabilistic models (DPMs) are widely adopted for their outstanding generative fidelity, yet their sampling is computationally demanding. Polynomial-based multistep samplers mitigate this cost by accelerating inference; however, despite their theoretical accuracy guarantees, they generate the sampling trajectory according to a predefined scheme, providing no flexibility for further optimization. To address this limitation, we propose RBF-Solver, a multistep diffusion sampler that interpolates model evaluations with Gaussian radial basis functions (RBFs). By leveraging learnable shape parameters in Gaussian RBFs, RBF-Solver explicitly follows optimal sampling trajectories. At first order, it reduces to the Euler method (DDIM). At second order or higher, as the shape parameters approach infinity, RBF-Solver converges to the Adams method, ensuring its compatibility with existing samplers. Owing to the locality of Gaussian RBFs, R

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Soochul Park, Yeon Ju Lee, SeongJin Yoon, Jiyub Shin, Juhee Lee, Seongwoon Jo · · 1 min read · 14 views
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arXiv:2603.13330v1 Announce Type: new Abstract: Diffusion probabilistic models (DPMs) are widely adopted for their outstanding generative fidelity, yet their sampling is computationally demanding. Polynomial-based multistep samplers mitigate this cost by accelerating inference; however, despite their theoretical accuracy guarantees, they generate the sampling trajectory according to a predefined scheme, providing no flexibility for further optimization. To address this limitation, we propose RBF-Solver, a multistep diffusion sampler that interpolates model evaluations with Gaussian radial basis functions (RBFs). By leveraging learnable shape parameters in Gaussian RBFs, RBF-Solver explicitly follows optimal sampling trajectories. At first order, it reduces to the Euler method (DDIM). At second order or higher, as the shape parameters approach infinity, RBF-Solver converges to the Adams method, ensuring its compatibility with existing samplers. Owing to the locality of Gaussian RBFs, RBF-Solver maintains high image fidelity even at fourth order or higher, where previous samplers deteriorate. For unconditional generation, RBF-Solver consistently outperforms polynomial-based samplers in the high-NFE regime (NFE >= 15). On CIFAR-10 with the Score-SDE model, it achieves an FID of 2.87 with 15 function evaluations and further improves to 2.48 with 40 function evaluations. For conditional ImageNet 256 x 256 generation with the Guided Diffusion model at a guidance scale 8.0, substantial gains are achieved in the low-NFE range (5-10), yielding a 16.12-33.73% reduction in FID relative to polynomial-based samplers.

Executive Summary

RBF-Solver, a novel multistep diffusion sampler for diffusion probabilistic models, leverages Gaussian radial basis functions to optimize sampling trajectories. By interpolating model evaluations with learnable shape parameters, RBF-Solver offers flexibility and compatibility with existing samplers. Empirical results demonstrate its superiority over polynomial-based samplers in terms of image fidelity and sampling efficiency. RBF-Solver's ability to converge to the Adams method at higher orders ensures its high-performance capabilities. With its potential to revolutionize diffusion probabilistic models, RBF-Solver presents a promising solution for demanding generative tasks. Its applicability in unconditional and conditional image generation showcases its versatility and effectiveness.

Key Points

  • ▸ RBF-Solver leverages Gaussian radial basis functions for optimal sampling trajectories
  • ▸ Compatibility with existing samplers through convergence to the Adams method
  • ▸ Superior performance over polynomial-based samplers in image fidelity and sampling efficiency

Merits

Strength in Optimizing Sampling Trajectories

RBF-Solver's ability to learn and optimize sampling trajectories using Gaussian radial basis functions enhances its flexibility and adaptability to diverse generative tasks.

Compatibility with Existing Samplers

RBF-Solver's convergence to the Adams method at higher orders ensures its seamless integration with existing diffusion probabilistic models.

Demerits

Potential Overhead in Computational Complexity

The learnable shape parameters in Gaussian RBFs might introduce additional computational overhead, which needs to be carefully managed to ensure efficient implementation.

Expert Commentary

RBF-Solver's innovative approach to optimizing sampling trajectories using Gaussian radial basis functions presents a significant advancement in the field of diffusion probabilistic models. By leveraging learnable shape parameters, RBF-Solver demonstrates its ability to adapt and optimize sampling trajectories, ensuring high-performance capabilities in both unconditional and conditional image generation. While the additional computational complexity of Gaussian RBFs needs to be carefully managed, RBF-Solver's potential to revolutionize diffusion probabilistic models makes it a highly promising solution for demanding generative tasks.

Recommendations

  • ✓ Further investigation into the computational overhead of Gaussian RBFs to ensure efficient implementation
  • ✓ Exploration of RBF-Solver's applicability in other domains, such as audio or video generation, to expand its scope and versatility

Sources

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