Deep learning models in medical imaging typically operate as parametric memory, diagnosing patients by recalling fixed knowledge learned during training. This contrasts sharply with clinical practice, where physicians employ analogical reasoning to diagnose new cases by referencing similar records from past exemplars. While In-Context Learning (ICL) frameworks such as Tabular Prior-Fitted Networks (TabPFN) offer a promising diagnosis-by-reference paradigm, they are designed with tabular-specific inductive priors and rely on non-differentiable preprocessing pipelines, leading to manifold mismatch and gradient fracture when applied to heterogeneous multimodal data. To address these limitations, we propose PromptDx, a novel diagnosis-by-reference framework that leverages a pre-trained TabPFN as an ICL engine while enabling seamless integration with multimodal representations. Our core contribution is a Differentiable Prompt Tuning (DPT) mechanism that aligns a Masked Multimodal Modeling module with the pre-trained ICL engine. By training a lightweight adapter as a differentiable surrogate for the engine's non-differentiable preprocessors, we enable an end-to-end optimization of multimodal prompts within the ICL paradigm. We validate our method on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset using 3D MRI and tabular biomarkers. Experiments demonstrate that our approach outperforms traditional parametric baselines. Notably, our method achieves superior performance using only 1% context samples compared to 30% in standard ICL, demonstrating exceptional manifold condensation ability. We further validate the generalizability of our DPT framework across six tabular datasets with diverse scales. Overall, our method offers a more data-efficient and clinically aligned paradigm for Alzheimer's Disease diagnosis.