G2T

Rotate a tissue slice, mirror it, slide it across the stage: nothing biological changes, because what survives every one of those motions is the set of distances between its cells. A model that reassembles dissociated cells by regressing 2-D coordinates must nonetheless commit to an arbitrary global frame at every denoising step, spending capacity on a degree of freedom that carries no signal. G2T (Gene-to-Tissue) moves the prediction onto the invariant itself.

G2T comes from the Theis and Lotfollahi groups, spanning the Wellcome Sanger Institute, Helmholtz Munich, the Technical University of Munich, and the Cambridge Stem Cell Institute at the University of Cambridge. It takes a slice's gene expression matrix as its only observed input and returns 2-D positions for every cell. The recipe descends directly from LUNA — an SE(2)-invariant pairwise squared-distance loss, a Transformer denoiser conditioned on generative time and on the current noisy positions — and changes what the denoiser emits. A Euclidean-distance-matrix (EDM) head produces per-cell embeddings in an eight-dimensional space, and the pairwise squared distances among those embeddings are the predicted geometry.

Predicting a distance matrix and recovering structure from it afterwards is the classical route of Euclidean-distance-matrix geometry, and mirrors the distogram step in AlphaFold 2. Here it lets the network route the prediction through more than two dimensions before the geometry is flattened back to a plane.

#Key Features

• Embedding-distance flow matching: The denoising target is a pairwise squared-distance matrix induced by K=8 per-cell embeddings, relaxing the 2-D output parameterisation of prior coordinate-denoising models while keeping the same clean target.
• Gene expression is the only observed input: At inference the coordinates the model conditions on are initialised from noise and evolved by the reverse process, never supplied, so a trained network applies unchanged to dissociated atlases that have no positions at all.
• Fast MDS read-out: A locally optimal block preconditioned (LOBPCG) eigensolver recovers only the top-2 eigenpairs of the double-centred Gram matrix, avoiding full O(N³) diagonalisation at every denoising step.
• Linear attention for whole sections: Efficient Attention with 32 heads is linear in cell count, letting sections of tens of thousands of cells be processed whole.
• Cross-platform transfer: Harmony integration over shared genes lets a model trained on imaging-based spatial transcriptomics run on scRNA-seq from a different platform.

#Technical Details

The network is an input MLP (G→256→256), eight Transformer blocks with 32-head Efficient Attention and a 256→256→256 feed-forward, an output MLP (256→256→32), and a linear EDM head (32→K=8); every block is conditioned on the flow-matching time and the noisy positions. Training uses straight-line probability paths, AdamW at lr 5×10⁻⁴ and an EMA of the weights, in PyTorch over AnnData. Two instances are reported. The cortex model takes the 254 quality-controlled genes of the 258-gene MERFISH panel and trains 1,000 epochs on 33 Donor-1 sections (158,379 cells) of the mouse primary motor cortex atlas, tested on 31 held-out Donor-2 sections (118,036 cells); Spearman correlation of pairwise-distance ranks rises from LUNA's 0.453 to 0.472, Contact F1 from 0.060 to 0.063, and per-cell-class Sum RSSD falls 1.6%. A cross-platform CNS model trains 3,500 epochs on 147 sections of the MERFISH whole-brain atlas and is applied to a 1.08M-cell dissociated CNS atlas through a 600-dimensional Harmony latent over 804 shared genes, reaching Spearman 0.180 and Contact F1 0.041; that reference is a STARmap PLUS-imputed spatial assignment rather than measured coordinates, so those figures are a relative method comparison. Ablations over ten seeds show that removing the EDM head worsens all three metrics, and that collapsing the embedding to K=2 is significantly worse than K=8 while K=16 is indistinguishable.

#Applications

The immediate use is retrofitting spatial context onto dissociated scRNA-seq, of which far more cells are archived than any spatial assay has produced. Reconstructed coordinates feed directly into the tooling that expects them — niche identification, cell–cell communication inference, tissue-architecture analysis — so a lab holding an atlas collected before spatial methods existed, or unable to afford a spatial run, can still ask spatial questions of it.

#Impact

G2T's contribution is a claim about parameterisation rather than about generative machinery: the ablations isolate the EDM head, not the switch from diffusion to flow matching, as the source of the accuracy gain, with flow matching cutting sampling from 1,000 steps to 50 at no measured cost. That makes embedding-distance prediction a reusable primitive for spatial-omics models beyond this one. The evidence is bounded: a preprint not yet peer reviewed, evaluated on mouse brain alone, with the transfer setting scored against an imputed reference. The authors also note that Contact F1 is computed on the closest 1% of cell pairs, where absolute values near 0.06 leave open whether local-contact fidelity suffices for a given downstream analysis. Code for the model and the paper's analyses is released under a BSD-3-Clause licence.