# Latent Fourier Transform

arXiv: https://arxiv.org/abs/2604.17986 · HTML: https://mlsanity.com/paper/2604.17986/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 69 of its 98 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 30 of 69)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [CNN Architectures for Large-Scale Audio Classification](https://mlsanity.com/paper/1609.09430/) (2016)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [AudioLM: a Language Modeling Approach to Audio Generation](https://mlsanity.com/paper/2209.03143/) (2022)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Simple and Controllable Music Generation](https://mlsanity.com/paper/2306.05284/) (2023)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [MusicLM: Generating Music From Text](https://mlsanity.com/paper/2301.11325/) (2023)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Masked Autoencoders that Listen](https://mlsanity.com/paper/2207.06405/) (2022)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [Diffsound: Discrete Diffusion Model for Text-to-sound Generation](https://mlsanity.com/paper/2207.09983/) (2022)
- [BigVGAN: A Universal Neural Vocoder with Large-Scale Training](https://mlsanity.com/paper/2206.04658/) (2022)

## Abstract (arXiv)

We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical patterns by timescale. By masking latents in the frequency domain during training, our method yields representations that can be manipulated coherently at inference. This allows us to generate musical variations and blends from reference examples while preserving characteristics at desired timescales, which are specified as frequencies in the latent space. LatentFT parallels the role of the equalizer in music production: while traditional equalizers operates on audible frequencies to shape timbre, LatentFT operates on latent-space frequencies to shape musical structure. Experiments and listening tests show that LatentFT improves condition adherence and quality compared to baselines. We also present a technique for hearing frequencies in the latent space in isolation, and show different musical attributes reside in different regions of the latent spectrum. Our results show how frequency-domain control in latent space provides an intuitive, continuous frequency axis for conditioning and blending, advancing us toward more interpretable and interactive generative music models.