Non-adiabatic dynamics is central to photochemistry, energy transfer, and electronically excited-state processes, but its interpretation depends strongly on the electronic representation. Tensor-network quantum dynamics uses a diabatic basis, but many important observables — and comparisons to mixed quantum-classical methods — are natural in the adiabatic basis. Directly adiabatising a high-dimensional wavefunction is infeasible: the transformation is a strongly geometry-dependent, high-rank object that cannot usually be represented compactly as a tensor operator. As a result, adiabatic observables have been difficult to obtain, even approximately.

Here, we introduce a sampling-based route to adiabatic observables from matrix product state wavefunctions. By adapting the sampling approach of Ferris and Vidal (A. Ferris & G. Vidal, Phys. Rev. B, 2012, 85), nuclear configurations are drawn efficiently from the density, and the local electronic wavefunction is then transformed. This bypasses the full adiabatisation of the wavefunction or any global fit of the transformation, and the resulting estimator is efficient, unbiased, error-bounded, requires no Markov chain, and suitable for generic Hamiltonians. We demonstrate the method on 24-dimensional pyrazine and a 78-dimensional BMA radical cation model, revealing large differences between diabatic and adiabatic population dynamics. More generally, this approach can be used to perform analysis on wavefunctions using tools normally reserved for trajectory-based methods, opening new avenues for understanding high-dimensional quantum simulations.