A Hybrid Wavelet-Fourier Method for Next-Generation Conditional Diffusion Models

• URL: http://arxiv.org/abs/2504.03821v1
• Date: Fri, 04 Apr 2025 17:11:04 GMT
• Title: A Hybrid Wavelet-Fourier Method for Next-Generation Conditional Diffusion Models
• Authors: Andrew Kiruluta, Andreas Lemos,
• Abstract summary: We present a novel generative modeling framework,Wavelet-Fourier-Diffusion, which adapts the diffusion paradigm to hybrid frequency representations.<n>We show how the hybrid frequency-based representation improves control over global coherence and fine texture synthesis.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 Fr\'echet 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.

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