Noise, Scores, and Straight Lines
Detailed notes on diffusion models and flow matching, from scores and SDEs through DDPM, probability-flow ODEs, guidance, and rectified flow.
Matthew Willetts
Machine learning researcher & founder · London
I'm a machine learning researcher, mostly working on generative models. My research has been published at NeurIPS (including an oral), ICLR and AISTATS. I did my DPhil in Computational Statistics & Machine Learning at Oxford, supervised by Chris Holmes and Stephen Roberts, then was a Research Fellow at UCL Computer Science with Brooks Paige and a Visiting Researcher at the Alan Turing Institute.
Most recently I co-founded QuantAMM, a venture-backed company turning investment strategies into autonomous, index-fund-style products; it was acquired in 2026. Alongside the usual commercial responsibilities of a founder and CEO, I designed the core mechanism and developed the underlying theory. I also built quantammsim, an open-source Python/JAX library for differentiable simulation, walk-forward backtesting, and gradient-based optimisation under real execution constraints. Before all of that I read Physics at Trinity College, Cambridge.
News
- May 2026QuantAMM was acquired.
- Mar 2026New preprint: Riemannian Geometry of Optimal Rebalancing in Dynamic Weight AMMs.
- Feb 2026New preprint: Pools as Portfolios — empirical rebalancing efficiency of live dynamic products.
- May 2025QuantAMM launched live autonomous rebalancing products, processing over $20M in trading volume.
- Nov 2024Open-sourced quantammsim, our Python/JAX library for differentiable simulation of AMM pools.
- Oct 2024Completed a series of four preprints on the theory of dynamic AMMs: closed-form arbitrage, optimal rebalancing, multistep frontrunning protections, and rebalancing-versus-rebalancing.
- Apr 2024QuantAMM closed a $1.85M pre-seed round led by 8VC.
- 2023Published the Temporal Function Market Making litepaper, the mechanism QuantAMM is built on.
- 2022A Multi-Resolution Framework for U-Nets accepted as an Oral at NeurIPS 2022.
- 2021Appointed Research Fellow at UCL Computer Science.
- 2021Awarded my DPhil in Computational Statistics & Machine Learning, Oxford.
Writing
- June 11, 2026 Beta's memory length in weighted least squares regression
- April 29, 2021 Improving VAEs' Robustness to Adversarial Attacks – Part 2/2
- February 7, 2021 Learning Independent Representations using Flows & Fixed Linear Models
Publications
* equal contribution
Thesis
Working Papers
Notes
Functions In, Functions Out
Detailed notes on neural operators as learned solution operators: DeepONets, FNOs, graph operators, low-rank variants, and physics-informed losses.
Software
quantammsim — an open-source Python/JAX library for differentiable simulation of trading strategies and gradient-based optimisation. Models market dynamics, arbitrage, spread and slippage; walk-forward backtesting, Bayesian calibration, and closed-form N-asset arbitrage solvers.