# Observation-Conditioned Latent Energy Priors for Sparse Implicit Neural Shape Completion

arXiv: https://arxiv.org/abs/2609.03694 · HTML: https://mlsanity.com/paper/2609.03694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 22 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Single-subject Multi-contrast MRI Super-resolution via Implicit Neural Representations](https://mlsanity.com/paper/2303.15065/) (2023)
- [MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision](https://mlsanity.com/paper/2308.16139/) (2023)
- [NISF: Neural Implicit Segmentation Functions](https://mlsanity.com/paper/2309.08643/) (2023)
- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [CINA: Conditional Implicit Neural Atlas for Spatio-Temporal Representation of Fetal Brains](https://mlsanity.com/paper/2403.08550/) (2024)
- [Implicit Neural Representations for Generative Modeling of Living Cell Shapes](https://mlsanity.com/paper/2207.06283/) (2022)
- [1-Lipschitz Neural Distance Fields](https://mlsanity.com/paper/2407.09505/) (2024)
- [MedFuncta: A Unified Framework for Learning Efficient Medical Neural Fields](https://mlsanity.com/paper/2502.14401/) (2025)

## Abstract (arXiv)

Implicit neural representations (INRs) can model continuous 3D shapes with a shared coordinate decoder and per-instance latent codes. At test time, autodecoder-style models commonly freeze the decoder and optimize a new latent code from sparse off-grid SDF samples. When these samples underconstrain inference, the latent can drift toward regions that fit the observations but decode implausible unobserved geometry. We propose a post-hoc observation-conditioned latent energy prior for frozen INR decoders. The energy scores standardized latents conditioned on a permutation-invariant encoding of the sparse observation set and is used as a residual expert alongside an L2 latent prior selected on validation data. We evaluate on a controlled cell-nucleus SDF dataset and a public MedShapeNet-derived SDF completion dataset. The proposed L2 objective augmented with conditional energy improves consistently over a validation-selected L2 baseline in the sparsest cell-nucleus regimes and, on MedShapeNet, outperforms both L2 and a six-component GMM latent-density prior across all reported readouts. A shuffled-context ablation is consistently weaker than matched context, supporting an observation-specific contribution. These results suggest that lightweight conditional energies can make pretrained INR decoders more observation-aware without retraining.