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

State estimation is a critical task in scientific, engineering and control applications. Since the reliability of reconstructions can depend on the number and position of sensors, Optimal sensor placement (OSP) is essential in scenarios where measurements are sparse and expensive. However, classical OSP approaches rely on Gaussian assumptions and are consequently unable to account for 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. Existing approaches to sensor selection either choose an unrealistically large number of sensors or employ strategies that emulate classical OSP methods. This results in a mismatch, wherein new models are paired with classical OSP tools, and motivates the need for fundamentally new ideas towards OSP that match the recent advances made in powerful recovery models. In this work, we introduce a distribution-free sensor placement framework based on the Christoffel function. Our main theoretical contributions introduce a mathematical formulation of optimal sampling and recovery guarantees for posterior sampling with arbitrary sensors and signal distributions. We use these to derive a new OSP strategy with non-asymptotic bounds on the number of sensors needed for recovery. Building on this, we develop \textbf{Christoffel-DPS}, with both offline and online variants, that implements nonparametric realizations of Christoffel sampling for generative models. As we show, Christoffel-DPS outperforms Gaussian OSP baselines and existing generative-model-based placement methods, validating that distribution-free sensing is both theoretically principled and practically superior. The framework is model agnostic, and 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.