# Optimal Sensor Placement via Graph-constrained Flow Matching

arXiv: https://arxiv.org/abs/2607.19831 · HTML: https://mlsanity.com/paper/2607.19831/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 0 of its 19 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Abstract (arXiv)

Optimal sensor placement is a fundamental problem in graph signal processing (GSP), where a limited number of sensors are deployed to reconstruct a continuous signal field. Existing GSP methods rely on combinatorial optimization over discretized graphs, resulting in high computational cost and sensor locations restricted to graph vertices. We reformulate sensor placement as a continuous-space generative modeling problem. An offline GSP optimization routine first generates training samples of optimal sensor configurations, from which a flow matching (FM) model learns their distribution. At inference, the learned velocity field directly generates continuous sensor coordinates, eliminating online combinatorial optimization. We further develop a permutation-invariant conditional generation framework for deployment with fixed anchor sensors. Experiments on a realistic radio propagation simulator demonstrate the effectiveness of the proposed framework for sensor placement.