Arbitrage-Constrained Diffusion-Inspired Denoising for Sparse Implied Volatility Surface Reconstruction

Sparse and noisy option quotes complicate implied-volatility surface construction, and statistical smoothing does not by itself enforce no-arbitrage structure. Building on arbitrage-regularized surface reconstruction, this paper develops a diffusion-inspired, noise-level-conditioned residual denoiser followed by an alternating shape-restoration step for normalized European call-price surfaces. On a risk-neutral benchmark of 1,280 surfaces on a 12×16 maturity–strike grid with 55% missing observations and additive noise, the method attains MAE 0.001886 and RMSE 0.002756 in normalized call-price units on 160 held-out surfaces and reduces measured calendar, strike-monotonicity, strike-bound and butterfly violations to zero at the stated tolerance, whereas the most accurate unconstrained denoiser (MAE 0.001679) leaves widespread butterfly violations. Implied-volatility diagnostics and a paired surface-level bootstrap further characterize the accuracy gains. The results quantify the accuracy–feasibility trade-off of combining learned denoising with explicit shape restoration and provide a transparent basis for arbitrage-consistent surface completion on market quotes.