Bayesian data assimilation (BDA) combines partial observations with physics-informed dynamical models to estimate latent system states. Filter-based BDA uses past and present data, enabling online forecasting, while smoothing additionally incorporates future observations for hindcasting and reanalysis. However, smoothing typically requires storing the full filter history and inverting filter statistics (e.g., covariance matrix), which is prohibitive in high-dimensional settings [1]. We introduce a framework leveraging the score-based structure of a backward diffusion flow, whose marginal distribution at any time matches the smoothing distribution when the terminal state follows the filter law [2]. This backward-in-time stochastic differential equation generates samples of the unobserved states consistent with the smoother distribution. For a broad class of nonlinear complex systems this equation admits a closed-form analytical expression [3], while for more general systems a Gaussian statistical approximation can be obtained via an ensemble Kalman–Bucy smoother [4]. These formulations enable training a neural network via score matching [5], alleviating the storage and computational costs of traditional smoother-based BDA. The trained score network can also generalize to unseen states, potentially enabling forward-in-time extrapolation. The developed methodology is demonstrated on high-dimensional systems with dense, temporally complex covariance structures arising from multiplicative and cross-correlated noise feedbacks and strongly nonlinear dynamics, achieving accurate smoothing while reducing memory and computational costs. [1] B. L. Rozovsky and S. V. Lototsky. Stochastic evolution systems: Linear theory and applications to non-linear filtering. Springer, 2018. [2] B. D. O. Anderson, A. N. Bishop, P. Del Moral and C. Palmier. Backward nonlinear smoothing diffusions. Theory of Probability & Its Applications, Vol. 66, No. 2, pp. 245–262, 2021. [3] M. Andreou and N. Chen. A martingale-free introduction to conditional Gaussian nonlinear systems. Entropy, Vol. 27, No. 1, Article 2, 2025. [4] Z. Jiang, M. Andreou and N. Chen. An ensemble Kalman-Bucy smoother for continuous-time data assimilation. Manuscript in preparation. [5] Y. Song, J. Sohl Dickstein, D. P. Kingma, A. Kumar, S. Ermon and B. Poole. Score based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020. doi: 10.48550/arXiv.2011.13456.