# Conformal Predictive Monitoring for Multi-Modal Scenarios

arXiv: https://arxiv.org/abs/2509.01338 · HTML: https://mlsanity.com/paper/2509.01338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [Conformal Prediction with Learned Features](https://mlsanity.com/paper/2404.17487/) (2024)
- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Robust Conformal Prediction for STL Runtime Verification under Distribution Shift](https://mlsanity.com/paper/2311.09482/) (2023)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Smoothed Model Checking for Uncertain Continuous Time Markov Chains](https://mlsanity.com/paper/1402.1450/) (2014)
- [Neural Predictive Monitoring under Partial Observability](https://mlsanity.com/paper/2108.07134/) (2021)
- [Time-Robust Control for STL Specifications](https://mlsanity.com/paper/2104.02677/) (2021)

## Built on by (most cited first, 1 of 1)

- [Guiding Neuro-Symbolic Scenario Generation with Spatio-Temporal Logic](https://mlsanity.com/paper/2605.19038/) (2026)

## Abstract (arXiv)

We consider the problem of quantitative predictive monitoring (QPM) of stochastic systems, i.e., predicting at runtime the degree of satisfaction of a desired temporal logic property from the current state of the system. Since computational efficiency is key to enable timely intervention against predicted violations, several state-of-the-art QPM approaches rely on fast machine-learning surrogates to provide prediction intervals for the satisfaction values, using conformal inference to offer statistical guarantees. However, these QPM methods suffer when the monitored agent exhibits multi-modal dynamics, whereby certain modes may yield high satisfaction values while others critically violate the property. Existing QPM methods are mode-agnostic and so would yield overly conservative and uninformative intervals that lack meaningful mode-specific satisfaction information. To address this problem, we present GenQPM, a method that leverages deep generative models, specifically score-based diffusion models, to reliably approximate the probabilistic and multi-modal system dynamics without requiring explicit model access. GenQPM employs a mode classifier to partition the predicted trajectories by dynamical mode. For each mode, we then apply conformal inference to produce statistically valid, mode-specific prediction intervals. We demonstrate the effectiveness of GenQPM on a benchmark of agent navigation and autonomous driving tasks, resulting in prediction intervals that are significantly more informative (less conservative) than mode-agnostic baselines.