Corrosion-induced crack widths provide critical insights into the corrosion of embedded steel reinforcements, offering a cost-effective approach to infer the distribution of steel weight loss in reinforced concrete (RC) structures. However, the stochastic relationship between corrosion-induced cracking and steel weight loss complicates the application of deterministic inference methods, especially when considering the spatial distributions of these two random variables. This paper proposes a Bayesian inference framework to estimate steel weight loss distributions in RC structures based on observed corrosion-induced crack widths. To address the computational challenges associated with the high dimensionality of steel weight loss distribution data, a Karhunen-Loève transform is utilized to extract the principal distribution features of steel weight loss, effectively reducing the dimensionality for Bayesian inference. A data-driven sequence-to-sequence transduction model is developed to predict corrosion-induced crack widths from steel weight loss, incorporating a novel nonlinear convolution kernel for input encoding and a sparse polynomial chaos expansion model for decoding. This model demonstrates superior accuracy and efficiency compared to finite element simulations and is employed as a forward model in the Bayesian inference process. The Hamiltonian Markov chain Monte Carlo (HMCMC) sampler is employed to efficiently sample from the high-dimensional posterior distribution. Numerical applications of the proposed method indicate that the Bayesian inference provides robust range estimations for the steel weight loss distribution, with the 95% confidence interval encompassing the majority of observations. Additionally, the method effectively infers high-dimensional sequences of steel weight loss up to 61 dimensions, achieved through the combination of dimension reduction techniques and the gradient-informed HMCMC sampler.