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
AI researcher · London
I do research at C5R, making frontier models better at experimental science. We build automated labs, and the simulations around them, where models run the whole scientific process and learn directly from reality.
I read Physics at Trinity College, Cambridge, then did a DPhil in Computational Statistics & Machine Learning at Oxford with Chris Holmes and Stephen Roberts, where I started working on generative models, and kept at it as a Senior Research Fellow at UCL Computer Science with Brooks Paige. I've published at NeurIPS (including an oral), ICLR and AISTATS.
After academia I co-founded and was CEO of Quantamm (acquired 2026), which turned investment strategies into autonomous, index-fund-style products. I ran the team, designed the core mechanism, raised a round led by 8VC, and took the company from concept to live products processing over $20M in trading volume.
Along the way I've also led the UK's team in a European Space Agency competition, putting a satellite the size of a drinks can on a rocket (we won); modelled hurricanes and how they flood New York's railways; and, with IDEO and Ford, built machine learning models that catch people breaking into vans by sound alone.
News
- Sep 2026At C5R we launched SciUniverse Level 1, our first benchmark: 92 lab tasks across chemistry, biology and materials science that frontier models carry out end to end in Facility-0, our model-run lab, by controlling instruments and instructing human operators (announcement).
- Aug 2026Joined C5R to do research.
- 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 Senior Research Fellow at UCL Computer Science.
- 2021Awarded my DPhil in Computational Statistics & Machine Learning, Oxford.
Writing
- October 2, 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.