  Diffusion models generating images conditionally on text, such as Dall-E 2
and Stable Diffusion, have recently made a splash far beyond the computer
vision community. Here, we tackle the related problem of generating point
clouds, both unconditionally, and conditionally with images. For the latter, we
introduce a novel geometrically-motivated conditioning scheme based on
projecting sparse image features into the point cloud and attaching them to
each individual point, at every step in the denoising process. This approach
improves geometric consistency and yields greater fidelity than current methods
relying on unstructured, global latent codes. Additionally, we show how to
apply recent continuous-time diffusion schemes. Our method performs on par or
above the state of art on conditional and unconditional experiments on
synthetic data, while being faster, lighter, and delivering tractable
likelihoods. We show it can also scale to diverse indoors scenes.
