Estimating causal effects in industrial time series requires handling temporal dynamics, time-varying treatments, and unobserved confounders. Existing causal foundation models (CausalPFN, CausalFM) operate only on static cross-sectional data; neural temporal methods (CRN, G-Net) require per-dataset training; and concurrent temporal-PFN proposals have not been demonstrated at industrial scale. None output explicit per-pair reliability signals alongside their CATE estimates. We introduce Temporal Causal Prior-Data Fitted Networks (TCPFN), a foundation model for zero-shot temporal causal discovery with learned reliability signals. TCPFN makes four contributions: (1) a Causal Judgment Head that jointly predicts null-effect probability, confounding strength, identifiability, mediation fraction, and causal regime; (2) a mixed training prior covering six causal regimes (independent, direct, confounded, mediated, time-varying confounded, feedback) plus CausalFM-style front-door and instrumental-variable priors; (3) a discrete-token panel-data architecture with cross-attention masking that prevents inter-horizon leakage; (4) zero-shot inference at industrial scale via FAISS-based context selection and one-step posterior correction. On 19 benchmark datasets across five domains, TCPFN achieves competitive zero-shot causal discovery: AUROC 0.96 on Tennessee Eastman, 0.93 on SWaT, 0.98 on Causal Rivers, 0.97 on CAUSRCA. The null detector reaches NullF1 0.94, AUROC 0.99. TCPFN scales to V=1,275 on a proprietary Kraft pulp-and-paper dataset in 6 hours on a single GPU; PCMCI, a CPU-only library, on a V=666 sub-panel of the same data took 81.5 hours, extrapolating by O(V^2) to ~12.5 days at V=1,275. TCPFN's top edges identify cross-subsystem causal relationships while PCMCI's surface within-instrument controller-measurement coupling -- a scalability case study.

Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by constraint-based causal discovery algorithms. BLITZ first removes broad smooth dependence on the conditioning set using low-order polynomial regression, then applies a small nonlinear feature map and residualizes those features with shallow tree regressions. The resulting statistic tests residual cross-covariance, with a moment-matched chi-square approximation to the null distribution. We show theoretically that the two-stage design reduces the effective complexity faced by the tree residualizers, allowing shallow trees to control residual conditional-mean bias while avoiding excessive overfitting. In simulations, BLITZ provides better null calibration than fast kernel, random-feature, and regression-based competitors while remaining among the fastest methods tested. In causal discovery experiments on synthetic graphs and flow-cytometry data, BLITZ yields more reliable endpoint orientations among retained adjacencies and competitive structural recovery. These results suggest that broad-to-local residualization is a practical route to calibrated, scalable nonparametric conditional independence testing for causal discovery.

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable d-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset.

Greedy Equivalence Search (GES) is a classic score-based algorithm for causal discovery from observational data. In the sample limit, it recovers the Markov equivalence class of graphs that describe the data. Still, it faces two challenges in practice: computational cost and finite-sample accuracy. In this paper, we develop Less Greedy Equivalence Search (LGES), a variant of GES that retains its theoretical guarantees while partially addressing these limitations. LGES modifies the greedy step; rather than always applying the highest-scoring insertion, it avoids edge insertions between variables for which the score implies some conditional independence.

Uncovering cause-effect relationships from observational time series is fundamental to understanding complex systems. While many methods infer static causal graphs, real-world systems often exhibit dynamic causality--where relationships evolve over time. Accurately capturing these temporal dynamics requires time-resolved causal graphs. We propose UnCLe, a novel deep learning method for scalable dynamic causal discovery. UnCLe employs a pair of Uncoupler and Recoupler networks to disentangle input time series into semantic representations and learns inter-variable dependencies via auto-regressive Dependency Matrices. It estimates dynamic causal influences by analyzing datapoint-wise prediction errors induced by temporal perturbations. Extensive experiments demonstrate that UnCLe not only outperforms state-of-the-art baselines on static causal discovery benchmarks but, more importantly, exhibits a unique capability to accurately capture and represent evolving temporal causality in both synthetic and real-world dynamic systems (e.g., human motion). UnCLe offers a promising approach for revealing the underlying, time-varying mechanisms of complex phenomena.

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.

Real-world datasets are often a combination of unobserved subpopulations that follow distinct causal generating processes. In an observational study, for example, participants may fall into unknown groups that either (a) respond effectively to a drug, or (b) show no response due to drug resistance. Not accounting for such heterogeneity then risks biased estimates of drug effectiveness. In this work, we formulate this setting through a causal mixture model, in which the data-generating process of each variable depends on latent group membership (a or b).

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of both linearly and nonlinearly coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-yourown coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.

Gene regulatory network inference (GRNI) aims to discover how genes causally regulate each other from gene expression data. It is well-known that statistical dependencies in observed data do not necessarily imply causation, as spurious dependencies may arise from latent confounders, such as non-coding RNAs. Numerous GRNI methods have thus been proposed to address this confounding issue. However, dependencies may also result from selection-only cells satisfying certain survival or inclusion criteria are observed-while these selection-induced spurious dependencies are frequently overlooked in gene expression data analyses. In this work, we show that such selection is ubiquitous and, when ignored or conflated with true regulations, can lead to flawed causal interpretation and misguided intervention recommendations. To address this challenge, a fundamental question arises: can we distinguish dependencies due to regulation, confounding, and crucially, selection? We show that gene perturbations offer a simple yet effective answer: selection-induced dependencies are symmetric under perturbation, while those from regulation or confounding are not. Building on this motivation, we propose GISL (Gene regulatory network Inference in the presence of Selection bias and Latent confounders), a principled algorithm that leverages perturbation data to uncover both true gene regulatory relations and non-regulatory mechanisms of selection and confounding up to the equivalence class. Experiments on synthetic and real-world gene expression data demonstrate the effectiveness of our method.