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