RBF-Solver: A Multistep Sampler for Diffusion Probabilistic Models via Radial Basis Functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912965721063424 |
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| author | Park, Soochul Lee, Yeon Ju Yoon, SeongJin Shin, Jiyub Lee, Juhee Jo, Seongwoon |
| author_facet | Park, Soochul Lee, Yeon Ju Yoon, SeongJin Shin, Jiyub Lee, Juhee Jo, Seongwoon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | RBF-Solver: A Multistep Sampler for Diffusion Probabilistic Models via Radial Basis Functions Park, Soochul Lee, Yeon Ju Yoon, SeongJin Shin, Jiyub Lee, Juhee Jo, Seongwoon Machine Learning Computer Vision and Pattern Recognition 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. |
| title | RBF-Solver: A Multistep Sampler for Diffusion Probabilistic Models via Radial Basis Functions |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2603.13330 |