# Conditional Tensor Diffusion: Distributional Counterfactual Learning and Inference

arXiv: https://arxiv.org/abs/2609.25924 · HTML: https://mlsanity.com/paper/2609.25924/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 124 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure](https://mlsanity.com/paper/2504.06566/) (2025)
- [Weighted Tensor Completion for Time-Series Causal Inference](https://mlsanity.com/paper/1902.04646/) (2019)
- [Causal Inference on Sequential Treatments via Tensor Completion](https://mlsanity.com/paper/2511.15866/) (2025)
- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [Tensor Completion for Causal Inference with Multivariate Longitudinal Data: A Reevaluation of COVID-19 Mandates](https://mlsanity.com/paper/2203.04689/) (2022)
- [Deep Bootstrap](https://mlsanity.com/paper/2602.10587/) (2026)
- [Spatial Causal Tensor Completion for Multiple Exposures and Outcomes: An Application to the Health Effects of PFAS Pollution](https://mlsanity.com/paper/2603.16854/) (2026)
- [CP-factorization for high dimensional tensor time series and double projection iterations](https://mlsanity.com/paper/2606.08560/) (2026)

## Abstract (arXiv)

Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop Counterfactual Tucker Diffusion (CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.