JaSpec-LID: Local Intrinsic Dimension Estimation via Jacobian Spectra of ODE-based Generative Models

Local intrinsic dimension (LID) quantifies the degrees of freedom of the data manifold around a point and is widely used to detect memorization, diagnose distribution shift, and characterize learned representations. Existing generative-model-based LID estimators are model-specific: they rely on a score, a log-density Hessian, or an exact log-likelihood, and therefore do not apply to ODE-based generators (flow matching, rectified flows, stochastic interpolants, and CNFs) that expose only a velocity field. We propose JaSpec, a model-agnostic LID estimator that counts the singular values of the velocity-field Jacobian $J_t = \partial f_\theta / \partial x$ that fall below a threshold $\tau$. JaSpec applies uniformly to score-based diffusion (via the probability-flow ODE) and to flow-based generators, and recovers Hessian-based estimators on probability-flow diffusion as a verification special case. We prove a direct dynamical identifiability theorem under a Jacobian-normal-dominance condition stated entirely in terms of $J_t$ and verified by an empirical spectral-gap diagnostic. On VP-SDE diffusion and OT-CFM flow-matching benchmarks with known LID, JaSpec attains MAE $= 0$ on most settings up to $D{=}3072$, where no prior model-based estimator reaches zero error, and improves over the strongest model-based baseline by an order of magnitude on the hardest $3072$-dimensional nonlinear mixture. We provide both an exact $\mathcal{O}(D^3)$ path and a linear-cost stochastic Lanczos quadrature path. JaSpec is, to our knowledge, the first LID estimator applicable to flow matching, rectified flows, and generic differentiable ODE generators.