Diffusion-based generative models generate samples by mapping noise to data via the reversal of a diffusion process which typically consists of the addition of independent Gaussian noise to every data coordinate. This diffusion process is, however, not well suited to the fundamental task of molecular conformer generation where the degrees of freedom differentiating conformers lie mostly in torsion angles. We, therefore, propose Torsional Diffusion that generates conformers by leveraging the definition of a diffusion process over the space SO(2)^n, a high dimensional torus representing torsion angles, and a novel SE(3) equivariant model capable of accurately predicting the score over this process. Empirically, we demonstrate that our model outperforms state-of-the-art methods on diversity metrics and performs competitively on precision ones. When compared to Gaussian diffusion models, Torsional Diffusion enables significantly more accurate generation while performing almost two orders of magnitude fewer inference time-steps.