Physics-Informed Diffusion Models for Flame Temperature Field Reconstruction via Differentiable Physics Proxies

Accurate reconstruction of flame temperature fields is critical for combustion diagnostics, industrial safety monitoring, and propulsion system analysis. Traditional methods, such as twocolor pyrometry and hyperspectral imaging, often suffer from sensitivity to noise, occlusion, and limited spatial resolution. While deep learning approaches like Convolutional Neural Networks (CNNs) have shown promise in regression tasks, they lack the generative capability to handle uncertainty and recover incomplete data. In this work, we propose a novel Flame Physics-Informed Diffusion Model (Flame-PIDM) framework for reconstructing flame temperature fields. Unlike standard data-driven generative models which may violate physical laws, our framework integrates a Differentiable Physics Proxy (DPP) - a neural network trained to approximate the complex mapping between radiative emission and temperature. This proxy is embedded directly into the diffusion training loop, imposing a strict consistency constraint between the generated visual appearance and the thermal field. We validate our approach on a synthetic flame dataset governed by non-linear thermal radiation laws. Experimental results demonstrate that our model generates high-fidelity temperature fields with a Pearson correlation coefficient greater than 0.99 against ground truth, maintaining strict adherence to physical constraints and significantly outperforming purely data-driven baselines.