# Deep Structural Causal Shape Models

arXiv: https://arxiv.org/abs/2208.10950 · HTML: https://mlsanity.com/paper/2208.10950/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Clinical and biomedical applications, one of 17 directions in LLM reasoning.
- Builds on 48 of its 80 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Placed in

- LLM reasoning / [Clinical and biomedical applications](https://mlsanity.com/lr/clinical-and-biomedical-applications/)

## Builds on (most cited first, 30 of 48)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [AttGAN: Facial Attribute Editing by Only Changing What You Want](https://mlsanity.com/paper/1711.10678/) (2017)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)

## Built on by (most cited first, 11 of 11)

- [Emerging Synergies in Causality and Deep Generative Models: A Survey](https://mlsanity.com/paper/2301.12351/) (2023)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [A Conditional Flow Variational Autoencoder for Controllable Synthesis of Virtual Populations of Anatomy](https://mlsanity.com/paper/2306.14680/) (2023)
- [Invariant Shape Representation Learning For Image Classification](https://mlsanity.com/paper/2411.12201/) (2024)
- [Applications of interpretable deep learning in neuroimaging: a comprehensive review](https://mlsanity.com/paper/2406.17792/) (2024)
- [Vector Representations of Vessel Trees](https://mlsanity.com/paper/2506.11163/) (2025)
- [Probabilistic Modelling is Sufficient for Causal Inference](https://mlsanity.com/paper/2512.23408/) (2025)
- [Generating Chest X-Ray Counterfactuals by Specialising Foundation Image Models](https://mlsanity.com/paper/2609.24879/) (2026)
- [Studying Therapy Effects and Disease Outcomes in Silico using Artificial Counterfactual Tissue Samples](https://mlsanity.com/paper/2302.03120/) (2023)
- [MoleCLUEs: Molecular Conformers Maximally In-Distribution for Predictive Models](https://mlsanity.com/paper/2306.11681/) (2023)
- [Shape Modeling of Longitudinal Medical Images: From Diffeomorphic Metric Mapping to Deep Learning](https://mlsanity.com/paper/2503.21489/) (2025)

## Abstract (arXiv)

Causal reasoning provides a language to ask important interventional and counterfactual questions beyond purely statistical association. In medical imaging, for example, we may want to study the causal effect of genetic, environmental, or lifestyle factors on the normal and pathological variation of anatomical phenotypes. However, while anatomical shape models of 3D surface meshes, extracted from automated image segmentation, can be reliably constructed, there is a lack of computational tooling to enable causal reasoning about morphological variations. To tackle this problem, we propose deep structural causal shape models (CSMs), which utilise high-quality mesh generation techniques, from geometric deep learning, within the expressive framework of deep structural causal models. CSMs enable subject-specific prognoses through counterfactual mesh generation ("How would this patient's brain structure change if they were ten years older?"), which is in contrast to most current works on purely population-level statistical shape modelling. We demonstrate the capabilities of CSMs at all levels of Pearl's causal hierarchy through a number of qualitative and quantitative experiments leveraging a large dataset of 3D brain structures.