Deep-sea sediment cores provide a key archive of past climate, with geochemical measurements of microfossils providing both environmental information and age constraints; however, constructing continuous age-depth models is challenging due to sparse and uncertain direct dating (e.g., radiocarbon up to 50 kyr BP) and the need to integrate more densely sampled but indirect proxies such as benthic δ¹⁸O, which requires pattern alignment to reference stacks while maintaining physically plausible sediment rates. Bayesian frameworks have therefore become standard, with approaches such as BACON (Blaauw and Christen, 2011) that models inverse sedimentation rates via an autoregressive gamma process and BIGMACS (Lee et al., 2023) that integrates both direct and indirect constraints through probabilistic alignment and empirically informed priors. Despite their practical utilities, these method exhibit key limitations: BACON relies heavily on user-specified hyperparameters that are not statistically inferred from the data, while BIGMACS could employ a sedimentation-rate model defined on uneven depth grids, potentially leading to inconsistent smoothness and sensitivity to proxy resolution. Here we propose the Cox-Ingersoll-Ross (CIR) Process Age Inference Algorithm to tackle the aforementioned limitations. This multi-layer Bayesian hierarchical framework employs the CIR process as a prior on the inverse sedimentation rates to guarantee a consistent smoothness over depths to address the drawback of BIGMACS, and it allows estimation of the CIR process model parameters via the Expectation-maximization (EM) algorithm. To validate our framework, we first estimated the model parameters from a carefully curated dataset of 79 radiocarbon records, and then applied the algorithm to four other radiocarbon-dated benthic δ¹⁸O sediment core records to compare the performance to BIGMACS. The resulting age models not only show greater consistency and robustness but also preserve smoothness of posterior sedimentation rates over depths and successfully avoid alignment artifacts.