Computational bottlenecks for denoising diffusions

ArXi:2503.08028v3 Announce Type: replace-cross Denoising diffusions sample from a probability distribution $\mu$ in $\mathbb{R}^d$ by constructing a stochastic process $({\hat{\boldsymbol x}}_t:t\ge 0)$ in $\mathbb{R}^d$ such that ${\hat{\boldsymbol x}}_0$ is easy to sample, but the distribution of $\hat{\boldsymbol x}_T$ at large $T$ approximates $\mu$. The drift ${\boldsymbol m}:\mathbb{R}^d\times\mathbb{R}\to\mathbb{R}^d$ of this diffusion process is learned my minimizing a score-matching objective.