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

arXiv: https://arxiv.org/abs/2504.03821 · HTML: https://mlsanity.com/paper/2504.03821/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)

## Built on by (most cited first, 5 of 5)

- [Learnable Multi-Scale Wavelet Transformer: A Novel Alternative to Self-Attention](https://mlsanity.com/paper/2504.08801/) (2025)
- [Virtual-mask Informed Prior for Sparse-view Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2504.07753/) (2025)
- [Wavelet-based Variational Autoencoders for High-Resolution Image Generation](https://mlsanity.com/paper/2504.13214/) (2025)
- [Spectral Regularization for Diffusion Models](https://mlsanity.com/paper/2603.02447/) (2026)
- [TriC-Motion: Tri-Domain Causal Modeling Grounded Text-to-Motion Generation](https://mlsanity.com/paper/2602.08462/) (2026)

## Abstract (arXiv)

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.