Semantic-Metric Bayesian Risk Fields: Learning Robot Safety from Human Videos with a VLM Prior

TL;DR

The paper tackles semantic, context-dependent safety by introducing a Bayesian risk framework that combines a VLM-derived prior with a learned likelihood from human demonstrations to produce pixel-dense, object-centric risk fields. These risk maps can serve as value signals for visuomotor planning or be lifted into 3D for traditional trajectory optimization, enabling human-aligned safety in new contexts. Empirical results show improved human alignment over strong vision-language baselines and demonstrate safer, context-aware trajectories in tabletop manipulation tasks, highlighting practical impact for risk-aware autonomous systems. The approach supports fast adaptation to new observations and rules via Bayesian updating and scales to larger datasets with a semantically rich risk representation.

Abstract

Humans interpret safety not as a binary signal but as a continuous, context- and spatially-dependent notion of risk. While risk is subjective, humans form rational mental models that guide action selection in dynamic environments. This work proposes a framework for extracting implicit human risk models by introducing a novel, semantically-conditioned and spatially-varying parametrization of risk, supervised directly from safe human demonstration videos and VLM common sense. Notably, we define risk through a Bayesian formulation. The prior is furnished by a pretrained vision-language model. In order to encourage the risk estimate to be more human aligned, a likelihood function modulates the prior to produce a relative metric of risk. Specifically, the likelihood is a learned ViT that maps pretrained features, to pixel-aligned risk values. Our pipeline ingests RGB images and a query object string, producing pixel-dense risk images. These images that can then be used as value-predictors in robot planning tasks or be projected into 3D for use in conventional trajectory optimization to produce human-like motion. This learned mapping enables generalization to novel objects and contexts, and has the potential to scale to much larger training datasets. In particular, the Bayesian framework that is introduced enables fast adaptation of our model to additional observations or common sense rules. We demonstrate that our proposed framework produces contextual risk that aligns with human preferences. Additionally, we illustrate several downstream applications of the model; as a value learner for visuomotor planners or in conjunction with a classical trajectory optimization algorithm. Our results suggest that our framework is a significant step toward enabling autonomous systems to internalize human-like risk. Code and results can be found at https://riskbayesian.github.io/bayesian_risk/.

Figures (8)

• Figure 1: Bayesian risk quantification attempts to model implicit human mental risk reasoning specifically in regards to pair-wise object interactions without unsafe examples such as manipulating knives near people or water above electronics. Risk depends on distance and object pair semantics. These two effects can be learned respectively through two different data streams: fine-grained life-experience or resource-intensive human demonstrations and coarse data derived from simple human queries or knowledge from foundational models. This decomposition of risk aligns well with a Bayesian interpretation, where risk corresponds to a posterior derived from a human data-driven, distance-based likelihood and a machine-driven, semantics-based common-sense prior.
• Figure 2: Top: RGB-D human demonstration videos are segmented and tracked. Middle: Per-trajectory inter-object distance histograms and their CDFs are extracted from the video streams. Bottom: DINOv3 features from the manipulated object and the scene are fed to the likelihood, predicts Bézier control points of a CDF.
• Figure 3: Dataset Generation: A prompt chain asks an LLM to list objects in particular settings, then score every pairwise combination for risk (1–5) with a hazard type and rationale. Model: Pixel features query an object lookup table for the nearest-neighbor object category. This label and the manipulated-object string is used in the risk lookup table to retrieve the correct risk ratings and reasoning.
• Figure 4: Ego-centric renders with corresponding manipulated object across different channels. Note that riskier objects are in red, while safer objects are in purple in accordance with the turbo colormap. In general, the posterior picks up risky objects from both the prior and likelihood, resulting in a more human-aligned risk image. More visualizations can be found on our https://riskbayesian.github.io/bayesian_risk/.
• Figure 5: Comparison of four trajectories from the Shelf environment while manipulating "cup". For each trajectory, we show the first, middle, and last frames alongside the value function. The value function corresponds to the P75 (seventy-fifth percentile) of the per-frame risk distribution, providing a robust summary of trajectory risk. Higher risk shelves produce consistently elevated values, illustrating human alignment of the proposed risk framework.

Theorems & Definitions (6)

• Theorem 1: Viability Consistency
• Corollary 1: Risk Consistency
• Remark 1
• Remark 2
• Remark 3
• Remark 4