# MorphoFlow: Sparse-Supervised Generative Shape Modeling with Adaptive Latent Relevance

arXiv: https://arxiv.org/abs/2604.11636 · HTML: https://mlsanity.com/paper/2604.11636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 19 of 19)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation](https://mlsanity.com/paper/1705.08302/) (2017)
- [ScribblePrompt: Fast and Flexible Interactive Segmentation for Any Biomedical Image](https://mlsanity.com/paper/2312.07381/) (2023)
- [A Survey on Label-efficient Deep Image Segmentation: Bridging the Gap between Weak Supervision and Dense Prediction](https://mlsanity.com/paper/2207.01223/) (2022)
- [Learning 3D Shape Completion under Weak Supervision](https://mlsanity.com/paper/1805.07290/) (2018)
- [Gaussian Process Morphable Models](https://mlsanity.com/paper/1603.07254/) (2016)
- [Interactive Medical Image Segmentation: A Benchmark Dataset and Baseline](https://mlsanity.com/paper/2411.12814/) (2024)
- [DeepSSM: A Blueprint for Image-to-Shape Deep Learning Models](https://mlsanity.com/paper/2110.07152/) (2021)
- [Mesh2SSM: From Surface Meshes to Statistical Shape Models of Anatomy](https://mlsanity.com/paper/2305.07805/) (2023)
- [ARD-VAE: A Statistical Formulation to Find the Relevant Latent Dimensions of Variational Autoencoders](https://mlsanity.com/paper/2501.10901/) (2025)
- [Point2SSM++: Self-Supervised Learning of Anatomical Shape Models from Point Clouds](https://mlsanity.com/paper/2405.09707/) (2024)
- [Weakly Supervised Bayesian Shape Modeling from Unsegmented Medical Images](https://mlsanity.com/paper/2405.09697/) (2024)
- [Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes](https://mlsanity.com/paper/2502.07145/) (2025)

## Abstract (arXiv)

Statistical shape modeling (SSM) is central to population level analysis of anatomical variability, yet most existing approaches rely on densely annotated segmentations and fixed latent representations. These requirements limit scalability and reduce flexibility when modeling complex anatomical variation. We introduce MorphoFlow, a sparse supervised generative shape modeling framework that learns compact probabilistic shape representations directly from sparse surface annotations. MorphoFlow integrates neural implicit shape representations with an autodecoder formulation and autoregressive normalizing flows to learn an expressive probabilistic density over the latent shape space. The neural implicit representation enables resolution-agnostic modeling of 3D anatomy, while the autodecoder formulation supports direct optimization of per-instance latent codes under sparse supervision. The autoregressive flow captures the distribution of latent anatomical variability providing a tractable, likelihood-based generative model of shapes. To promote compact and structured latent representations, we incorporate adaptive latent relevance weighting through sparsity-inducing priors, enabling the model to regulate the contribution of individual latent dimensions according to their relevance to the underlying anatomical variation while preserving generative expressivity. The resulting latent space supports uncertainty quantification and anatomically plausible shape synthesis without manual latent dimensionality tuning. Evaluation on publicly available lumbar vertebrae and femur datasets demonstrates accurate high-resolution reconstruction from sparse inputs and recovery of structured modes of anatomical variation consistent with population level trends.