Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling

Robert Gruhlke introduced a solver for Hamilton-Jacobi-Bellman equations in diffusion models using the functional tensor train format. The method leverages latent low-rank structures to approximate high-dimensional functions, enabling model compression and rapid computation. Integrated with a backward-in-time iterative scheme derived from backward stochastic differential equations, the approach addresses training time and hyperparameter sensitivity issues found in existing techniques like PINNs, achieving efficient sampling from complex target distributions.