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Measurement of the red damping wing of neutral hydrogen in quasar spectraprovides a probe of the epoch of reionization in the early Universe. Suchquantification requires precise and unbiased estimates of the intrinsiccontinua near Lyman-$\alpha$ (Ly$\alpha$), a challenging task given the highlyvariable Ly$\alpha$ emission profiles of quasars. Here, we introduce a fullyprobabilistic approach to intrinsic continua prediction. We frame the problemas a conditional density estimation task and explicitly model the distributionover plausible blue-side continua ($1190\ \unicode{xC5} \leq\lambda_{\text{rest}} < 1290\ \unicode{xC5}$) conditional on the red-sidespectrum ($1290\ \unicode{xC5} \leq \lambda_{\text{rest}} < 2900\\unicode{xC5}$) using normalizing flows. Our approach achieves state-of-the-artprecision and accuracy, allows for sampling one thousand plausible continua inless than a tenth of a second, and can natively provide confidence intervals onthe blue-side continua via Monte Carlo sampling. We measure the damping wingeffect in two $z>7$ quasars and estimate the volume-averaged neutral fractionof hydrogen from each, finding $\bar{x}_\text{HI}=0.304 \pm 0.042$ for ULASJ1120+0641 ($z=7.09$) and $\bar{x}_\text{HI}=0.384 \pm 0.133$ for ULASJ1342+0928 ($z=7.54$).

Fully probabilistic quasar continua predictions near Lyman-{\alpha} with conditional neural spline flows