A Hybrid Wavelet-Fourier Method for Next-Generation Conditional Diffusion Models
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arXiv
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| Format: | Preprint |
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2025
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| author | Kiruluta, Andrew Lemos, Andreas |
| author_facet | Kiruluta, Andrew Lemos, Andreas |
| contents | We present a novel generative modeling framework,Wavelet-Fourier-Diffusion, which adapts the diffusion paradigm to hybrid frequency representations in order to synthesize high-quality, high-fidelity images with improved spatial localization. In contrast to conventional diffusion models that rely exclusively on additive noise in pixel space, our approach leverages a multi-transform that combines wavelet sub-band decomposition with partial Fourier steps. This strategy progressively degrades and then reconstructs images in a hybrid spectral domain during the forward and reverse diffusion processes. By supplementing traditional Fourier-based analysis with the spatial localization capabilities of wavelets, our model can capture both global structures and fine-grained features more effectively. We further extend the approach to conditional image generation by integrating embeddings or conditional features via cross-attention. Experimental evaluations on CIFAR-10, CelebA-HQ, and a conditional ImageNet subset illustrate that our method achieves competitive or superior performance relative to baseline diffusion models and state-of-the-art GANs, as measured by Fréchet Inception Distance (FID) and Inception Score (IS). We also show how the hybrid frequency-based representation improves control over global coherence and fine texture synthesis, paving the way for new directions in multi-scale generative modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hybrid Wavelet-Fourier Method for Next-Generation Conditional Diffusion Models Kiruluta, Andrew Lemos, Andreas Computer Vision and Pattern Recognition Machine Learning Image and Video Processing We present a novel generative modeling framework,Wavelet-Fourier-Diffusion, which adapts the diffusion paradigm to hybrid frequency representations in order to synthesize high-quality, high-fidelity images with improved spatial localization. In contrast to conventional diffusion models that rely exclusively on additive noise in pixel space, our approach leverages a multi-transform that combines wavelet sub-band decomposition with partial Fourier steps. This strategy progressively degrades and then reconstructs images in a hybrid spectral domain during the forward and reverse diffusion processes. By supplementing traditional Fourier-based analysis with the spatial localization capabilities of wavelets, our model can capture both global structures and fine-grained features more effectively. We further extend the approach to conditional image generation by integrating embeddings or conditional features via cross-attention. Experimental evaluations on CIFAR-10, CelebA-HQ, and a conditional ImageNet subset illustrate that our method achieves competitive or superior performance relative to baseline diffusion models and state-of-the-art GANs, as measured by Fréchet Inception Distance (FID) and Inception Score (IS). We also show how the hybrid frequency-based representation improves control over global coherence and fine texture synthesis, paving the way for new directions in multi-scale generative modeling. |
| title | A Hybrid Wavelet-Fourier Method for Next-Generation Conditional Diffusion Models |
| topic | Computer Vision and Pattern Recognition Machine Learning Image and Video Processing |
| url | https://arxiv.org/abs/2504.03821 |