  Powerful priors allow us to perform inference with insufficient information.
In this paper, we propose an autoregressive prior for 3D shapes to solve
multimodal 3D tasks such as shape completion, reconstruction, and generation.
We model the distribution over 3D shapes as a non-sequential autoregressive
distribution over a discretized, low-dimensional, symbolic grid-like latent
representation of 3D shapes. This enables us to represent distributions over 3D
shapes conditioned on information from an arbitrary set of spatially anchored
query locations and thus perform shape completion in such arbitrary settings
(e.g., generating a complete chair given only a view of the back leg). We also
show that the learned autoregressive prior can be leveraged for conditional
tasks such as single-view reconstruction and language-based generation. This is
achieved by learning task-specific naive conditionals which can be approximated
by light-weight models trained on minimal paired data. We validate the
effectiveness of the proposed method using both quantitative and qualitative
evaluation and show that the proposed method outperforms the specialized
state-of-the-art methods trained for individual tasks. The project page with
code and video visualizations can be found at
https://yccyenchicheng.github.io/AutoSDF/.
