  Score-based generative models (SGMs) have demonstrated remarkable synthesis
quality. SGMs rely on a diffusion process that gradually perturbs the data
towards a tractable distribution, while the generative model learns to denoise.
The complexity of this denoising task is, apart from the data distribution
itself, uniquely determined by the diffusion process. We argue that current
SGMs employ overly simplistic diffusions, leading to unnecessarily complex
denoising processes, which limit generative modeling performance. Based on
connections to statistical mechanics, we propose a novel critically-damped
Langevin diffusion (CLD) and show that CLD-based SGMs achieve superior
performance. CLD can be interpreted as running a joint diffusion in an extended
space, where the auxiliary variables can be considered "velocities" that are
coupled to the data variables as in Hamiltonian dynamics. We derive a novel
score matching objective for CLD and show that the model only needs to learn
the score function of the conditional distribution of the velocity given data,
an easier task than learning scores of the data directly. We also derive a new
sampling scheme for efficient synthesis from CLD-based diffusion models. We
find that CLD outperforms previous SGMs in synthesis quality for similar
network architectures and sampling compute budgets. We show that our novel
sampler for CLD significantly outperforms solvers such as Euler--Maruyama. Our
framework provides new insights into score-based denoising diffusion models and
can be readily used for high-resolution image synthesis. Project page and code:
https://nv-tlabs.github.io/CLD-SGM.
