  Probabilistic diffusion models have achieved state-of-the-art results for
image synthesis, inpainting, and text-to-image tasks. However, they are still
in the early stages of generating complex 3D shapes. This work proposes
Diffusion-SDF, a generative model for shape completion, single-view
reconstruction, and reconstruction of real-scanned point clouds. We use neural
signed distance functions (SDFs) as our 3D representation to parameterize the
geometry of various signals (e.g., point clouds, 2D images) through neural
networks. Neural SDFs are implicit functions and diffusing them amounts to
learning the reversal of their neural network weights, which we solve using a
custom modulation module. Extensive experiments show that our method is capable
of both realistic unconditional generation and conditional generation from
partial inputs. This work expands the domain of diffusion models from learning
2D, explicit representations, to 3D, implicit representations.
