As discussed in Section 3.4 of the main paper, our proposed loss term Here "D" stands for "decay". We designed our ablation study with DiGS. Normal C. Chamfer F-Score mean std. We have two primary reasons for this choice. Firstly, our primary interest lies in the 0-isosurface rather than other level sets.

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we propose Diffusive Gibbs Sampling (DiGS), an innovative family of sampling methods designed for effective sampling from distributions characterized by distant and disconnected modes. DiGS integrates recent developments in diffusion models, leveraging Gaussian convolution to create an auxiliary noisy distribution that bridges isolated modes in the original space and applying Gibbs sampling to alternately draw samples from both spaces. Our approach exhibits a better mixing property for sampling multi-modal distributions than state-of-the-art methods such as parallel tempering. We demonstrate that our sampler attains substantially improved results across various tasks, including mixtures of Gaussians, Bayesian neural networks and molecular dynamics.

Neural shape representations have recently shown to be effective in shape analysis and reconstruction tasks. Existing neural network methods require point coordinates and corresponding normal vectors to learn the implicit level sets of the shape. Normal vectors are often not provided as raw data, therefore, approximation and reorientation are required as pre-processing stages, both of which can introduce noise. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal shape representation networks that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and show state-of-the-art performance compared to other unoriented methods and on-par performance compared to oriented methods.