# Differentiable Digital Signal Processing Mixture Model-Guided Diffusion for Synthesis Parameter Estimation from Harmonic Sound Mixtures

arXiv: https://arxiv.org/abs/2609.14427 · HTML: https://mlsanity.com/paper/2609.14427/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 15 of its 17 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Neural Audio Synthesis of Musical Notes with WaveNet Autoencoders](https://mlsanity.com/paper/1704.01279/) (2017)
- [DDSP: Differentiable Digital Signal Processing](https://mlsanity.com/paper/2001.04643/) (2020)
- [CREPE: A Convolutional Representation for Pitch Estimation](https://mlsanity.com/paper/1802.06182/) (2018)
- [RAVE: A variational autoencoder for fast and high-quality neural audio synthesis](https://mlsanity.com/paper/2111.05011/) (2021)
- [CRASH: Raw Audio Score-based Generative Modeling for Controllable High-resolution Drum Sound Synthesis](https://mlsanity.com/paper/2106.07431/) (2021)
- [MIDI-DDSP: Detailed Control of Musical Performance via Hierarchical Modeling](https://mlsanity.com/paper/2112.09312/) (2021)
- [A Review of Differentiable Digital Signal Processing for Music & Speech Synthesis](https://mlsanity.com/paper/2308.15422/) (2023)
- [Latent Diffusion Bridges for Unsupervised Musical Audio Timbre Transfer](https://mlsanity.com/paper/2409.06096/) (2024)
- [Zimtohrli: An Efficient Psychoacoustic Audio Similarity Metric](https://mlsanity.com/paper/2509.26133/) (2025)
- [Expressive Acoustic Guitar Sound Synthesis with an Instrument-Specific Input Representation and Diffusion Outpainting](https://mlsanity.com/paper/2401.13498/) (2024)
- [Differentiable Digital Signal Processing Mixture Model for Synthesis Parameter Extraction from Mixture of Harmonic Sounds](https://mlsanity.com/paper/2202.00200/) (2022)

## Abstract (arXiv)

A differentiable digital signal processing (DDSP) autoencoder reconstructs a monophonic harmonic sound through three types of synthesis parameters: fundamental frequency, loudness, and timbre features. To handle mixtures of harmonic sounds within the DDSP approach, we have previously proposed a DDSP mixture model (DDSPMM). It represents a mixture as the sum of source signals synthesized by the decoders of pretrained DDSP autoencoders. Although DDSPMM enables direct estimation of synthesis parameters of each source from mixtures, it does not explicitly model temporal variations in the synthesis parameters and can produce excessive temporal fluctuations. In this paper, we propose a method for estimating synthesis parameters with temporally plausible trajectories by incorporating a denoising diffusion probabilistic model (DDPM) into the DDSPMM-based estimation. The DDPM is trained as a generative model of synthesis parameters. During estimation, the proposed method guides the DDPM reverse diffusion process with the reconstruction error between the observed mixture and the mixture synthesized by DDSPMM from the current estimates. Experiments on woodwind and string instrument ensembles showed that the DDPM-based regularization improves synthesis parameter estimation by imposing temporal plausibility on the estimated trajectories.