Control-Ready Uncertainty for Trajectory Diffusion

Zhiwei Xue, Jia Yue Kam, Jinhang Qiu, Yifeng Cheng, Ege Gursoy, Jiaming Wang, Vincent Bonnet, Harold Soh · N/A · 2026

Summary

Abstract Summary

Diffusion models can represent complex, multimodal trajectory distributions, but extracting uncertainty from them typically requires costly Monte Carlo sampling. This limits their use in real-time control, where robots must rapidly assess risk and maintain safety margins. We introduce Score-Curvature for Online Precision Estimation (SCOPE), a lightweight module that augments diffusion trajectory models with control-ready uncertainty. SCOPE learns a structured precision matrix around each nominal trajectory by distilling score-curvature information and producing calibrated Gaussian tubes with low overhead and without repeated Monte Carlo sampling. These tubes provide per-timestep covariance estimates that can be used both as predicted occupancy for moving agents and as adaptive exploration guides for robot control. We evaluate SCOPE with mode-conditioned multimodal diffusion backbones in pedestrian forecasting, crowd navigation, Maze2D control, and real-world Franka Panda manipulation. Across these settings, SCOPE provides fast uncertainty estimation, which leads to better closed-loop performance. Project page: https://zackaxue.github.io/SCOPE-project-page/

Key Points

Diffusion models can represent complex, multimodal trajectory distributions, but extracting uncertainty from them typically requires costly Monte Carlo sampling.
This limits their use in real-time control, where robots must rapidly assess risk and maintain safety margins.
We introduce Score-Curvature for Online Precision Estimation (SCOPE), a lightweight module that augments diffusion trajectory models with control-ready uncertainty.
SCOPE learns a structured precision matrix around each nominal trajectory by distilling score-curvature information and producing calibrated Gaussian tubes with low overhead and without repeated Monte Carlo sampling.
These tubes provide per-timestep covariance estimates that can be used both as predicted occupancy for moving agents and as adaptive exploration guides for robot control.

Preliminaries

Diffusion models as trajectory forecasters. Diffusion models generate trajectories by learning to reverse a gradual noising process.

The forward process progressively corrupts a clean trajectory $\mathbf{y}_{0}$ into Gaussian noise over $\mathsf{S}$ steps, with closed form $q(\mathbf{y}_{\mathsf{s}}/\mathbf{y}_{0})=\mathcal{N}\!\big(\sqrt{\bar{\alpha}_{\mathsf{s}}}\,\mathbf{y}_{0},\,(1-\bar{\alpha}_{\mathsf{s}})\mathbf{I}\big)$, where $\bar{\alpha}_{\mathsf{s}}=\prod_{j=1}^{\mathsf{s}}\alpha_{j}$ and $\alpha_{j}\in(0,1)$ is a noise schedule.

Preliminaries — Control-Ready Uncertainty for Trajectory Diffusion — Figure 1: ( Top ) SCOPE leverages score curvature to augment diffusion predictions with precision tubes that are suitable for control. It provides uncertainty estimates at low computation cost, enabling real-time control. ( Bottom ) We apply SCOPE as a robot policy prior in MPPI and also to predict the trajectories of other agents.

Score-Curvature for Online Precision Estimation (SCOPE)

This section presents SCOPE, a lightweight module for extracting local, control-ready uncertainty from diffusion trajectory models. Given a conditioning context $\mathbf{c}$—such as agent histories, scene geometry, start and goal states, or task information—a diffusion model can produce one or more nominal future trajectories.

SCOPE augments each nominal trajectory with a structured precision matrix, whose inverse defines a local Gaussian tube around that prediction.

Score-Curvature for Online Precision Estimation (SCOPE) — Control-Ready Uncertainty for Trajectory Diffusion — Figure 2: SCOPE overview. Our method extracts control-ready Gaussian tubes from a diffusion predictor. Here, we use a multimodal diffusion backbone (left) that produces $K$ nominal trajectories with explicit mode probabilities. The SCOPE Precision Head (right) wraps each trajectory in a structured precision matrix $\boldsymbol{\Lambda}_{k}$, learned by distilling the score model’s terminal curvature via Hessian-vector products at training time. At inference, Gaussian tubes are produced with low overhead after diffusion decoding.

Experiments

Our experiments are designed to answer three questions: (Q1) Does SCOPE produce accurate uncertainty tubes with fast inference, compared to sampling-based alternatives? (Q2) When used for policy, does SCOPE improve MPPI rollout efficiency and downstream control performance? (Q3) When used as a predictive world model, does SCOPE improve downstream control in interactive scenarios?

We evaluate SCOPE on pedestrian trajectory forecasting in an ORCA-simulated Y-corridor environment [ 41 ] (Fig.

Experiments — Control-Ready Uncertainty for Trajectory Diffusion — Figure 3: ( Left ) Y-corridor environment. ( Right ) Uncertainty quality (NLL).

Sources and Demonstrations

Figures are reproduced from Xue et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.