# SMD-Nets: Stereo Mixture Density Networks

arXiv: https://arxiv.org/abs/2104.03866 · HTML: https://mlsanity.com/paper/2104.03866/

## Key facts

- Cited by 120 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 59 references that are in the map.
- First posted on arXiv 8 Apr 2021.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [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)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [PointRend: Image Segmentation as Rendering](https://mlsanity.com/paper/1912.08193/) (2019)
- [Cascade Cost Volume for High-Resolution Multi-View Stereo and Stereo Matching](https://mlsanity.com/paper/1912.06378/) (2019)
- [End-to-End Learning of Geometry and Context for Deep Stereo Regression](https://mlsanity.com/paper/1703.04309/) (2017)
- [GA-Net: Guided Aggregation Net for End-to-end Stereo Matching](https://mlsanity.com/paper/1904.06587/) (2019)
- [Group-wise Correlation Stereo Network](https://mlsanity.com/paper/1903.04025/) (2019)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [3D Photography using Context-aware Layered Depth Inpainting](https://mlsanity.com/paper/2004.04727/) (2020)
- [AANet: Adaptive Aggregation Network for Efficient Stereo Matching](https://mlsanity.com/paper/2004.09548/) (2020)
- [Pseudo-LiDAR++: Accurate Depth for 3D Object Detection in Autonomous Driving](https://mlsanity.com/paper/1906.06310/) (2019)
- [Stereo Matching by Training a Convolutional Neural Network to Compare Image Patches](https://mlsanity.com/paper/1510.05970/) (2015)
- [Hierarchical Deep Stereo Matching on High-resolution Images](https://mlsanity.com/paper/1912.06704/) (2019)
- [DeepPruner: Learning Efficient Stereo Matching via Differentiable PatchMatch](https://mlsanity.com/paper/1909.05845/) (2019)
- [Hierarchical Discrete Distribution Decomposition for Match Density Estimation](https://mlsanity.com/paper/1812.06264/) (2018)
- [StereoNet: Guided Hierarchical Refinement for Real-Time Edge-Aware Depth Prediction](https://mlsanity.com/paper/1807.08865/) (2018)
- [SegStereo: Exploiting Semantic Information for Disparity Estimation](https://mlsanity.com/paper/1807.11699/) (2018)
- [Real-time self-adaptive deep stereo](https://mlsanity.com/paper/1810.05424/) (2018)
- [Occlusions, Motion and Depth Boundaries with a Generic Network for Disparity, Optical Flow or Scene Flow Estimation](https://mlsanity.com/paper/1808.01838/) (2018)

## Built on by (most cited first, 30 of 120)

- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [Depth Pro: Sharp Monocular Metric Depth in Less Than a Second](https://mlsanity.com/paper/2410.02073/) (2024)
- [MapAnything: Universal Feed-Forward Metric 3D Reconstruction](https://mlsanity.com/paper/2509.13414/) (2025)
- [MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Details](https://mlsanity.com/paper/2507.02546/) (2025)
- [AnySplat: Feed-forward 3D Gaussian Splatting from Unconstrained Views](https://mlsanity.com/paper/2505.23716/) (2025)
- [FoundationStereo: Zero-Shot Stereo Matching](https://mlsanity.com/paper/2501.09898/) (2025)
- [WonderJourney: Going from Anywhere to Everywhere](https://mlsanity.com/paper/2312.03884/) (2023)
- [MUSt3R: Multi-view Network for Stereo 3D Reconstruction](https://mlsanity.com/paper/2503.01661/) (2025)
- [Rethinking Depth Estimation for Multi-View Stereo: A Unified Representation](https://mlsanity.com/paper/2201.01501/) (2022)
- [EPro-PnP: Generalized End-to-End Probabilistic Perspective-n-Points for Monocular Object Pose Estimation](https://mlsanity.com/paper/2303.12787/) (2023)
- [WorldMirror: Universal 3D World Reconstruction with Any-Prior Prompting](https://mlsanity.com/paper/2510.10726/) (2025)
- [IGEV++: Iterative Multi-range Geometry Encoding Volumes for Stereo Matching](https://mlsanity.com/paper/2409.00638/) (2024)
- [Pixel-Perfect Depth with Semantics-Prompted Diffusion Transformers](https://mlsanity.com/paper/2510.07316/) (2025)
- [RoMa v2: Harder Better Faster Denser Feature Matching](https://mlsanity.com/paper/2511.15706/) (2025)
- [Open Challenges in Deep Stereo: the Booster Dataset](https://mlsanity.com/paper/2206.04671/) (2022)
- [Stereo Anywhere: Robust Zero-Shot Deep Stereo Matching Even Where Either Stereo or Mono Fail](https://mlsanity.com/paper/2412.04472/) (2024)
- [NeRF-Supervised Deep Stereo](https://mlsanity.com/paper/2303.17603/) (2023)
- [Dens3R: A Foundation Model for 3D Geometry Prediction](https://mlsanity.com/paper/2507.16290/) (2025)
- [PatchFusion: An End-to-End Tile-Based Framework for High-Resolution Monocular Metric Depth Estimation](https://mlsanity.com/paper/2312.02284/) (2023)
- [MixNeRF: Modeling a Ray with Mixture Density for Novel View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2302.08788/) (2023)
- [Neural Markov Random Field for Stereo Matching](https://mlsanity.com/paper/2403.11193/) (2024)
- [LingBot-Map: Geometric Context Transformer for Streaming 3D Reconstruction](https://mlsanity.com/paper/2604.14141/) (2026)
- [Booster: a Benchmark for Depth from Images of Specular and Transparent Surfaces](https://mlsanity.com/paper/2301.08245/) (2023)
- [PlaneDepth: Self-supervised Depth Estimation via Orthogonal Planes](https://mlsanity.com/paper/2210.01612/) (2022)
- [DUNE: Distilling a Universal Encoder from Heterogeneous 2D and 3D Teachers](https://mlsanity.com/paper/2503.14405/) (2025)
- [OpenStereo: A Comprehensive Benchmark for Stereo Matching and Strong Baseline](https://mlsanity.com/paper/2312.00343/) (2023)
- [VGGT-Omega](https://mlsanity.com/paper/2605.15195/) (2026)
- [DA2: Depth Anything in Any Direction](https://mlsanity.com/paper/2509.26618/) (2025)
- [A Survey on Deep Stereo Matching in the Twenties](https://mlsanity.com/paper/2407.07816/) (2024)
- [InfiniDepth: Arbitrary-Resolution and Fine-Grained Depth Estimation with Neural Implicit Fields](https://mlsanity.com/paper/2601.03252/) (2026)

## Abstract (arXiv)

Despite stereo matching accuracy has greatly improved by deep learning in the last few years, recovering sharp boundaries and high-resolution outputs efficiently remains challenging. In this paper, we propose Stereo Mixture Density Networks (SMD-Nets), a simple yet effective learning framework compatible with a wide class of 2D and 3D architectures which ameliorates both issues. Specifically, we exploit bimodal mixture densities as output representation and show that this allows for sharp and precise disparity estimates near discontinuities while explicitly modeling the aleatoric uncertainty inherent in the observations. Moreover, we formulate disparity estimation as a continuous problem in the image domain, allowing our model to query disparities at arbitrary spatial precision. We carry out comprehensive experiments on a new high-resolution and highly realistic synthetic stereo dataset, consisting of stereo pairs at 8Mpx resolution, as well as on real-world stereo datasets. Our experiments demonstrate increased depth accuracy near object boundaries and prediction of ultra high-resolution disparity maps on standard GPUs. We demonstrate the flexibility of our technique by improving the performance of a variety of stereo backbones.