# GraphMDN: Leveraging graph structure and deep learning to solve inverse problems

arXiv: https://arxiv.org/abs/2010.13668 · HTML: https://mlsanity.com/paper/2010.13668/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

## Built on by (most cited first, 26 of 26)

- [MHFormer: Multi-Hypothesis Transformer for 3D Human Pose Estimation](https://mlsanity.com/paper/2111.12707/) (2021)
- [Probabilistic Monocular 3D Human Pose Estimation with Normalizing Flows](https://mlsanity.com/paper/2107.13788/) (2021)
- [Diffusion-Based 3D Human Pose Estimation with Multi-Hypothesis Aggregation](https://mlsanity.com/paper/2303.11579/) (2023)
- [DiffPose: Multi-hypothesis Human Pose Estimation using Diffusion models](https://mlsanity.com/paper/2211.16487/) (2022)
- [GFPose: Learning 3D Human Pose Prior with Gradient Fields](https://mlsanity.com/paper/2212.08641/) (2022)
- [Hierarchical Kinematic Probability Distributions for 3D Human Shape and Pose Estimation from Images in the Wild](https://mlsanity.com/paper/2110.00990/) (2021)
- [Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views](https://mlsanity.com/paper/2304.06024/) (2023)
- [DiffuPose: Monocular 3D Human Pose Estimation via Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2212.02796/) (2022)
- [HuManiFlow: Ancestor-Conditioned Normalising Flows on SO(3) Manifolds for Human Pose and Shape Distribution Estimation](https://mlsanity.com/paper/2305.06968/) (2023)
- [FinePOSE: Fine-Grained Prompt-Driven 3D Human Pose Estimation via Diffusion Models](https://mlsanity.com/paper/2405.05216/) (2024)
- [Multi-hypothesis 3D human pose estimation metrics favor miscalibrated distributions](https://mlsanity.com/paper/2210.11179/) (2022)
- [ManiPose: Manifold-Constrained Multi-Hypothesis 3D Human Pose Estimation](https://mlsanity.com/paper/2312.06386/) (2023)
- [CHAMP: Conformalized 3D Human Multi-Hypothesis Pose Estimators](https://mlsanity.com/paper/2407.06141/) (2024)
- [GTA-Net: An IoT-Integrated 3D Human Pose Estimation System for Real-Time Adolescent Sports Posture Correction](https://mlsanity.com/paper/2411.06725/) (2024)
- [Graph Neural Networks in Computer Vision -- Architectures, Datasets and Common Approaches](https://mlsanity.com/paper/2212.10207/) (2022)
- [Utilizing Uncertainty in 2D Pose Detectors for Probabilistic 3D Human Mesh Recovery](https://mlsanity.com/paper/2411.16289/) (2024)
- [Platypose: Calibrated Zero-Shot Multi-Hypothesis 3D Human Motion Estimation](https://mlsanity.com/paper/2403.06164/) (2024)
- [FMPose3D: monocular 3D pose estimation via flow matching](https://mlsanity.com/paper/2602.05755/) (2026)
- [Flow Matching for Probabilistic Monocular 3D Human Pose Estimation](https://mlsanity.com/paper/2601.16763/) (2026)
- [Spatio-temporal MLP-graph network for 3D human pose estimation](https://mlsanity.com/paper/2308.15313/) (2023)
- [Diffusion-based Pose Refinement and Muti-hypothesis Generation for 3D Human Pose Estimaiton](https://mlsanity.com/paper/2401.04921/) (2024)
- [Probablistic Restoration with Adaptive Noise Sampling for 3D Human Pose Estimation](https://mlsanity.com/paper/2405.02114/) (2024)
- [Social EgoMesh Estimation](https://mlsanity.com/paper/2411.04598/) (2024)
- [GazeD: Context-Aware Diffusion for Accurate 3D Gaze Estimation](https://mlsanity.com/paper/2601.12948/) (2026)
- [UST-Hand: An Uncertainty-aware Spatiotemporal Point Cloud Interaction Network for 3D Self-supervised Hand Pose Estimation](https://mlsanity.com/paper/2605.17742/) (2026)
- [CQF-HMR: Continuous Quaternion Flows for Probabilistic 3D Human Mesh Recovery from a Single Image](https://mlsanity.com/paper/2609.00995/) (2026)

## Abstract (arXiv)

The recent introduction of Graph Neural Networks (GNNs) and their growing popularity in the past few years has enabled the application of deep learning algorithms to non-Euclidean, graph-structured data. GNNs have achieved state-of-the-art results across an impressive array of graph-based machine learning problems. Nevertheless, despite their rapid pace of development, much of the work on GNNs has focused on graph classification and embedding techniques, largely ignoring regression tasks over graph data. In this paper, we develop a Graph Mixture Density Network (GraphMDN), which combines graph neural networks with mixture density network (MDN) outputs. By combining these techniques, GraphMDNs have the advantage of naturally being able to incorporate graph structured information into a neural architecture, as well as the ability to model multi-modal regression targets. As such, GraphMDNs are designed to excel on regression tasks wherein the data are graph structured, and target statistics are better represented by mixtures of densities rather than singular values (so-called ``inverse problems"). To demonstrate this, we extend an existing GNN architecture known as Semantic GCN (SemGCN) to a GraphMDN structure, and show results from the Human3.6M pose estimation task. The extended model consistently outperforms both GCN and MDN architectures on their own, with a comparable number of parameters.