A Fourier Space Perspective on Diffusion Models
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
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| _version_ | 1866915289953730560 |
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| author | Falck, Fabian Pandeva, Teodora Zahirnia, Kiarash Lawrence, Rachel Turner, Richard Meeds, Edward Zazo, Javier Karmalkar, Sushrut |
| author_facet | Falck, Fabian Pandeva, Teodora Zahirnia, Kiarash Lawrence, Rachel Turner, Richard Meeds, Edward Zazo, Javier Karmalkar, Sushrut |
| contents | Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the standard Denoising Diffusion Probabilistic Models (DDPM) forward process of additive white noise, this property results in high-frequency components being corrupted faster and earlier in terms of their Signal-to-Noise Ratio (SNR) than low-frequency ones. The reverse process then generates low-frequency information before high-frequency details. In this work, we study the inductive bias of the forward process of diffusion models in Fourier space. We theoretically analyse and empirically demonstrate that the faster noising of high-frequency components in DDPM results in violations of the normality assumption in the reverse process. Our experiments show that this leads to degraded generation quality of high-frequency components. We then study an alternate forward process in Fourier space which corrupts all frequencies at the same rate, removing the typical frequency hierarchy during generation, and demonstrate marked performance improvements on datasets where high frequencies are primary, while performing on par with DDPM on standard imaging benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fourier Space Perspective on Diffusion Models Falck, Fabian Pandeva, Teodora Zahirnia, Kiarash Lawrence, Rachel Turner, Richard Meeds, Edward Zazo, Javier Karmalkar, Sushrut Machine Learning Computer Vision and Pattern Recognition Methodology Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the standard Denoising Diffusion Probabilistic Models (DDPM) forward process of additive white noise, this property results in high-frequency components being corrupted faster and earlier in terms of their Signal-to-Noise Ratio (SNR) than low-frequency ones. The reverse process then generates low-frequency information before high-frequency details. In this work, we study the inductive bias of the forward process of diffusion models in Fourier space. We theoretically analyse and empirically demonstrate that the faster noising of high-frequency components in DDPM results in violations of the normality assumption in the reverse process. Our experiments show that this leads to degraded generation quality of high-frequency components. We then study an alternate forward process in Fourier space which corrupts all frequencies at the same rate, removing the typical frequency hierarchy during generation, and demonstrate marked performance improvements on datasets where high frequencies are primary, while performing on par with DDPM on standard imaging benchmarks. |
| title | A Fourier Space Perspective on Diffusion Models |
| topic | Machine Learning Computer Vision and Pattern Recognition Methodology |
| url | https://arxiv.org/abs/2505.11278 |