# Stable Differentiable Causal Discovery

arXiv: https://arxiv.org/abs/2311.10263 · HTML: https://mlsanity.com/paper/2311.10263/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 23 of 23)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Scaling structural learning with NO-BEARS to infer causal transcriptome networks](https://mlsanity.com/paper/1911.00081/) (2019)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Optimizing NOTEARS Objectives via Topological Swaps](https://mlsanity.com/paper/2305.17277/) (2023)

## Built on by (most cited first, 30 of 31)

- [Extremely Greedy Equivalence Search](https://mlsanity.com/paper/2502.19551/) (2025)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [CauScale: Neural Causal Discovery at Scale](https://mlsanity.com/paper/2602.08629/) (2026)
- [Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm](https://mlsanity.com/paper/2405.18314/) (2024)
- [Arrow: A Foundation Model for Causal Discovery](https://mlsanity.com/paper/2605.07204/) (2026)
- [Since Faithfulness Fails: The Performance Limits of Neural Causal Discovery](https://mlsanity.com/paper/2502.16056/) (2025)
- [Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generation](https://mlsanity.com/paper/2509.24798/) (2025)
- [TabCausal: Pretraining Across Causal Environments for Tabular Causal Discovery](https://mlsanity.com/paper/2605.31156/) (2026)
- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [Efficient Differentiable Discovery of Causal Order](https://mlsanity.com/paper/2410.08787/) (2024)
- [Coarse-to-Fine Learning of Dynamic Causal Structures](https://mlsanity.com/paper/2602.22532/) (2026)
- [Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyond](https://mlsanity.com/paper/2410.18396/) (2024)
- [Amortized Causal Discovery with Prior-Fitted Networks](https://mlsanity.com/paper/2512.11840/) (2025)
- [KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data](https://mlsanity.com/paper/2606.10358/) (2026)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)
- [Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models](https://mlsanity.com/paper/2408.10976/) (2024)
- [Differentiable Structure Learning and Causal Discovery for General Binary Data](https://mlsanity.com/paper/2509.21658/) (2025)
- [Large-Scale Bayesian Causal Discovery with Interventional Data](https://mlsanity.com/paper/2510.01562/) (2025)
- [Theoretical Guarantees for Causal Discovery on Large Random Graphs](https://mlsanity.com/paper/2511.02536/) (2025)
- [DAG Learning from Zero-Inflated Count Data Using Continuous Optimization](https://mlsanity.com/paper/2512.16233/) (2025)
- [SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphs](https://mlsanity.com/paper/2602.02830/) (2026)
- [Neural Autoregressive Flows for Markov Boundary Learning](https://mlsanity.com/paper/2603.20791/) (2026)
- [Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives](https://mlsanity.com/paper/2604.02250/) (2026)
- [When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Data](https://mlsanity.com/paper/2605.04930/) (2026)
- [PACER: Acyclic Causal Discovery from Large-Scale Interventional Data](https://mlsanity.com/paper/2605.15353/) (2026)
- [Amortized Bayesian Causal Discovery of Extended Factor Graphs](https://mlsanity.com/paper/2607.22934/) (2026)
- [Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates](https://mlsanity.com/paper/2608.08103/) (2026)
- [Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discovery](https://mlsanity.com/paper/2609.03442/) (2026)
- [CausalArena: Benchmarking Causal Discovery in the Foundation Model Era](https://mlsanity.com/paper/2609.11897/) (2026)

## Abstract (arXiv)

Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the search as a continuous optimization. But existing DCD methods are numerically unstable, with poor performance beyond tens of variables. In this paper, we propose Stable Differentiable Causal Discovery (SDCD), a new method that improves previous DCD methods in two ways: (1) It employs an alternative constraint for acyclicity; this constraint is more stable, both theoretically and empirically, and fast to compute. (2) It uses a training procedure tailored for sparse causal graphs, which are common in real-world scenarios. We first derive SDCD and prove its stability and correctness. We then evaluate it with both observational and interventional data and on both small-scale and large-scale settings. We find that SDCD outperforms existing methods in both convergence speed and accuracy and can scale to thousands of variables. We provide code at https://github.com/azizilab/sdcd.