Felix Nannesson Meli: Mixture Variational Interpolant Flow Matching for 3-Dimensional Spatial Transcriptomics Reconstruction

Abstract: Spatial transcriptomics makes it possible to measure gene expression directly on intact tissue slices, preserving the spatial context that is lost in standard bulk RNA sequencing. Each measurement, however, is a two-dimensional map, while biological tissue is fundamentally three-dimensional. Full three-dimensional reconstruction therefore requires serial sectioning of the tissue into consecutive layers, with each slice sequenced separately. The cost of sequencing and the physical damage caused by slicing make dense sampling infeasible, so experiments rely on sparse sampling that leaves gaps along the depth axis of the tissue. This thesis studies the problem of predicting the unmeasured intermediate slices from a series of observed tissue sections, and formulates it as a multi-marginal generative modeling problem in which every observed slice is a marginal distribution of an underlying continuous process.

In this thesis, a generative model is proposed that combines multi-marginal flow matching with a variational mixture interpolant. Instead of connecting the observed slices with a piecewise linear path, intermediate states are sampled from a variational mixture distribution conditioned on the end slices. The mixture parameters are produced by a correction network that deforms a linear interpolant, and are trained with a novel evidence lower bound objective. They are then used to condition the flow matching velocity field during the training phase. The resulting interpolant is flexible and multi-modal, granting the complexity to model the branching and looping structures typical of biological structures.

The method is evaluated on two reconstruction tasks, a left-out slices experiment and a sparse reconstruction experiment simulating low resolution sampling. These experiments are run on a two-dimensional dataset of Drosophila embryo tissue, and compare it against a baseline flow matching model using a piecewise linear interpolant on earth mover’s distance (EMD).

The baseline performs slightly better on average, and the proposed method exhibits sensitivity to hyperparameter choice and some instability in the mixture variance during training. When anomalous training runs are excluded, the variational mixture interpolant outperforms the baseline, and both methods produce trajectories that faithfully represent the data. The results indicate that variational mixture interpolants are a promising direction for three-dimensional spatial transcriptomics reconstruction, and point to future work on stabilizing the variance modeling and scaling the approach to real, high-dimensional transcriptomics data.