Checklist USA-NA-AIO 2026 Round 2 · Task 3
Diffusion Models
Derive the forward-process marginals and the KL-based training objective of a one-dimensional diffusion model.
The task
Problem 3 (50 points, 'non open-ended') studies a one-dimensional diffusion model: proving that x_t given x_0 is Gaussian and finding its mean and variance and their limits; the KL divergence between two Gaussians; the true posterior q(x_{t−1} | x_t, x_0); the noise-prediction parameterisation of the reverse mean and the resulting KL; and, conceptually, how to feed the time step t into the noise-prediction network.
Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You submit
- One notebook named Diffusion_LastName_FirstName_SchoolName with all derivations.
- Format
- 2026 USA-NA-AIO Round 2, Day 2 (5 April 2026).