mlsanityData to 14 Oct 2026

Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions

arXiv 2605.06861 ↗First posted 7 May 2026cs.LG cs.NA math.NAcited by 0

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

State estimation is a critical task in scientific, engineering and control applications. Since the reliability of reconstructions depends on the number and position of sensors, optimal sensor placement (OSP) is essential in scenarios where measurements are sparse and expensive. Classical OSP approaches rely on Gaussian assumptions and are consequently unable to account for the complex distributions encountered in many real-world systems. Generative-model-based reconstruction using sensor guided diffusion posterior sampling (DPS) has emerged as a promising technique for reconstructing states from highly complex distributions. However, existing sensor-selection methods either require unrealistically many sensors or emulate classical OSP, creating a mismatch between modern recovery models with classical OSP tools motivating the need for fundamentally new ideas towards OSP that match the recent advances made in powerful recovery models. We introduce a distribution-free sensor placement framework based on the Christoffel function: a mathematical formulation of optimal sampling and recovery guarantees for posterior sampling with arbitrary sensors and signal distributions, from which we derive a new OSP strategy with non-asymptotic bounds on the number of sensors needed for recovery. We develop Christoffel-DPS, with offline and online variants, instantiating Christoffel sampling for generative models. Christoffel-DPS outperforms Gaussian OSP baselines and existing generative-model placement methods, validating that distribution-free sensing is both theoretically principled and practically superior. The framework is model-agnostic; we demonstrate its application to a range of unconditional DPS and flow-matching models on structurally non-Gaussian benchmarks, showing the efficacy of Christoffel-DPS in low sensor budget regimes.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 27 of its 42 references that are in the map. First posted on arXiv 7 May 2026.

Builds on

27 of 42 references.

Closest ancestors · 2

Same direction, newest first

  1. 2026Decoupled Diffusion Sampling for Inverse Problems on Function Spaces30 Jan
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 25

  1. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 108
  4. 2023Score-based Diffusion Models in Function Spacecited by 82
  5. 2017Data-Driven Sparse Sensor Placement for Reconstructioncited by 57
  6. 2021Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learningcited by 57
  7. 2021Instance-Optimal Compressed Sensing via Posterior Samplingcited by 43
  8. 2013A Statistical Perspective on Algorithmic Leveragingcited by 39
  9. 2023Infinite-Dimensional Diffusion Modelscited by 39
  10. 2025Reduced Order Modeling with Shallow Recurrent Decoder Networkscited by 24
  11. 2024Diffusion Models as Cartoonists: The Curious Case of High Density Regionscited by 21
  12. 2025Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approachcited by 12
13 more
  1. 2023CS4ML: A general framework for active learning with arbitrary data based on Christoffel functionscited by 11
  2. 2025PhySense: Sensor Placement Optimization for Accurate Physics Sensingcited by 11
  3. 2025Guiding diffusion models to reconstruct flow fields from sparse datacited by 11
  4. 2024Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurementscited by 9
  5. 2025Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observationscited by 9
  6. 2015A statistical perspective of sampling scores for linear regressioncited by 5
  7. 2025Graph Transformers for inverse physics: reconstructing flows around arbitrary 2D airfoilscited by 5
  8. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problemscited by 5
  9. 2023Data-Induced Interactions of Sparse Sensors Using Statistical Physicscited by 3
  10. 2025PySensors 2.0: A Python Package for Sparse Sensor Placementcited by 3
  11. 2026Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systemscited by 3
  12. 2025How many measurements are enough? Bayesian recovery in inverse problems with general distributionscited by 2
  13. 2026GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domainscited by 1

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