MIT 6.S184 Lab 1 has three parts. First you write the step functions for Euler and Euler–Maruyama. Then you use them to simulate Brownian motion and the Ornstein–Uhlenbeck process and watch how σ and θ shape trajectories and the final distribution. Finally you implement Langevin dynamics, watch a cloud of points get pushed toward a five-mode Gaussian mixture, and show by hand that the OU process is Langevin dynamics with a Gaussian target. The questions, code scaffolding, and official solutions are all on GitHub; outside readers get no Gradescope grading and have to check against the solutions themselves.
Lab 2 turns §3–4 of the notes into PyTorch. You implement the Gaussian conditional path, its conditional vector field, and its conditional score. Then two nearly identical trainers do flow matching and score matching, Proposition 1 converts the learned vector field into a score, and finally a linear path makes a ring distribution flow into a checkerboard. Everything runs on 2D toy data. The README records a diffusion-coefficient bug fix dated 1/11/26; when I checked on 2026-09-30, the fix appeared only in the solutions notebook, not the student version, so patch it yourself before you start.
A score function is the gradient of the log density; it points toward where probability rises fastest. On Gaussian paths, the score and last lecture's vector field are both linear in x and z, so each converts into the other (Proposition 1 in the notes): learn one and you have learned both. With the score in hand, you can add noise of any strength to the ODE and turn it into an SDE without changing the distribution at any time (Theorem 17). The score itself is learned with the same trick as flow matching, by regressing on the conditional score. On Gaussian paths, that amounts to predicting the noise that was added, which is the DDPM training objective.