Multiparametric MRI is increasingly recommended as a first-line noninvasive approach to detect and localize prostate cancer, requiring at minimum diffusion-weighted (DWI) and T2-weighted (T2w) MR sequences. Early machine learning attempts using only T2w images have shown promising diagnostic performance in segmenting radiologist-annotated lesions. Such uni-modal T2-only approaches deliver substantial clinical benefits by reducing costs and expertise required to acquire other sequences. This work investigates an arguably more challenging application using only T2w at inference, but to localize individual cancers based on independent histopathology labels. We formulate DWI images as a latent modality (readily available during training) to classify cancer presence at local Barzell zones, given only T2w images as input. In the resulting expectation-maximization algorithm, a latent modality generator (implemented using a flow matching-based generative model) approximates the latent DWI image posterior distribution in the E-steps, while in M-steps a cancer localizer is simultaneously optimized with the generative model to maximize the expected likelihood of cancer presence. The proposed approach provides a novel theoretical framework for learning from a privileged DWI modality, yielding superior cancer localization performance compared to approaches that lack training DWI images or existing frameworks for privileged learning and incomplete modalities. The proposed T2-only methods perform competitively or better than baseline methods using multiple input sequences (e.g., improving the patient-level F1 score by 14.4\% and zone-level QWK by 5.3\% over the T2w+DWI baseline). We present quantitative evaluations using internal and external datasets from 4,133 prostate cancer patients with histopathology-verified labels.