Measurement of the red damping wing of neutral hydrogen in quasar spectra provides a probe of the epoch of reionization in the early Universe . Such quantification requires precise and unbiased estimates of the intrinsic continua near Lyman- \alpha ( Ly \alpha ) , a challenging task given the highly variable Ly \alpha emission profiles of quasars . Here , we introduce a fully probabilistic approach to intrinsic continua prediction . We frame the problem as a conditional density estimation task and explicitly model the distribution over plausible blue-side continua ( \SI { 1190 } { \angstrom } \leq \lambda _ { \text { rest } } < \SI { 1290 } { \angstrom } ) conditional on the red-side spectrum ( \SI { 1290 } { \angstrom } \leq \lambda _ { \text { rest } } < \SI { 2900 } { \angstrom } ) using normalizing flows . Our approach achieves state-of-the-art precision and accuracy , allows for sampling one thousand plausible continua in less than a tenth of a second , and can natively provide confidence intervals on the blue-side continua via Monte Carlo sampling . We measure the damping wing effect in two z > 7 quasars and estimate the volume-averaged neutral fraction of hydrogen from each , finding \bar { x } _ { \text { HI } } = 0.304 \pm 0.042 for ULAS J1120+0641 ( z = 7.09 ) and \bar { x } _ { \text { HI } } = 0.384 \pm 0.133 for ULAS J1342+0928 ( z = 7.54 ) .