High-Fidelity Monte Carlo Reconstruction from Finite-Photon Simulations with a Photon-Budget-Conditioned Volumetric State-Space Model

High-fidelity Monte Carlo (MC) simulation demands substantial sampling effort. We make the photon budget an explicit conditioning variable for learned reconstruction, allowing one volumetric model to adapt across eight sampling regimes while retaining MC as the forward solver. Photon-budget affine modulation coordinates directional spatial gating with Fourier-domain Mamba-3 processing. On a three-dimensional skin-lesion benchmark, the model improves mean PSNR by 4.82 dB over the strongest macro-average baseline (configuration-paired 95% interval: [4.57, 5.07] dB). Gains extend to inverse-transformed field summaries and tested held-out physical regimes, with capacity-matched controls supporting the design. Reconstruction from $10^3$ photons exceeds raw $10^6$-photon MC in mean PSNR, SSIM, and RMSE against matched references, using $1000\times$ fewer input photons. At $10^6$ photons, MC plus inference achieves an $8.09\times$ same-GPU speedup over direct $10^8$-photon MC, with a 0.67-dB mean PSNR gap against independent $10^9$-photon references; a separate CPU-MC/GPU-inference workflow gives approximately $106\times$ timing speedup at the same budgets. These results establish photon-budget conditioning as a practical route to efficient volumetric MC reconstruction and motivate using known sampling effort as a design variable for learned correction in scientific simulation.