FlowAlign uses learned paths to align different kinds of data

Two measurements of the same cell can reveal different aspects of its biology. RNA sequencing measures gene expression, while ATAC sequencing measures chromatin accessibility. Aligning these measurements computationally means more than placing similar cell types together: ideally, each cell’s ATAC representation should also land near its own RNA counterpart.

A November 6, 2026 arXiv preprint by Ruizhi Yuan and colleagues proposes FlowAlign for this kind of problem. One modality defines a fixed representation space, and a model learns to map the other into it. The researchers test whether their method can improve individual matching while retaining the target space’s useful organization.

Learning paths, then using them as a training signal

FlowAlign separates training into two stages. First, it learns a source-conditioned velocity field from paired examples. For each pair, the method samples a starting point near the source representation and constructs a straight interpolation path to the known target representation. A neural network learns the velocity required along that path, receiving the path location, interpolation time and source representation as inputs.

These paths are mathematical constructions between vectors, not observed biological trajectories. The source and target vectors must share a dimensionality for path construction, but they need not already share an aligned coordinate system.

Next, the velocity network is frozen. A separate mapper proposes a target-space position for each source sample. FlowAlign constructs paths to that proposed position and measures how closely their required velocities agree with the frozen field. This disagreement becomes the mapper’s training loss.

Although the second-stage loss does not explicitly use the paired target, its guidance still comes from paired supervision: those targets trained the velocity field. The loss can work alone or supplement an existing model’s objective.

At prediction time, the field and path sampling are discarded. The trained source-side model produces its target-space representation in a single forward pass, without numerically following the learned flow.

Better matching in the reported tests

The synthetic experiment illustrates why distributional agreement and individual accuracy are different goals. A distribution-matching baseline best reproduced the chosen target marginal distribution but had much larger paired errors. FlowAlign achieved the lowest endpoint and latent-position errors among the four tested methods, though it did not achieve the best distribution-matching score.

For single-cell experiments, the researchers used paired peripheral-blood and bone-marrow datasets, termed PBMC and BMMC. ATAC and RNA measurements were reduced to 25-dimensional representations, with RNA defining the fixed target coordinates. Cells were divided into 80% training, 10% validation and 10% test sets; prediction used only the ATAC side.

On PBMC, FlowAlign retrieved the exact paired RNA cell as the nearest neighbor in 14.1% of test cases, compared with 11.0% for direct squared-error regression. On BMMC, it reached 5.0%, versus 3.2% for regression and 3.8% for the strongest alternative paired mapper on that metric. These gains also show a remaining difficulty: most exact cell matches were still missed.

Cell-type label transfer was substantially easier than exact matching. FlowAlign reached 92.0% on PBMC and 83.6% on BMMC. Clustering-agreement measures also favored it over the architecture-matched paired baselines, although its cross-modality mixing score was not uniformly best.

The comparison needs qualification. Established integration methods were evaluated in their own aligned spaces, whereas FlowAlign and the controlled regression baselines used the fixed RNA space. The architecture-matched comparisons therefore more directly isolate the effect of the training objective.

A separate bird image–text experiment mapped DINOv3 image features into a fixed space derived from SigLIP2 text features, with both independently reduced to 128 dimensions. FlowAlign achieved 7.5% exact-pair retrieval, versus 6.7% for direct regression, and led the evaluated methods on all three reported metrics.

What the evidence does—and does not—establish

The theoretical analysis links a low path-consistency loss to small endpoint error when the frozen field is accurate and satisfies a local smoothness assumption. It also gives a local interpretation in which different error directions receive different penalties. These are conditional results, not guarantees that every trained model preserves neighborhoods. Held-out field diagnostics supported discrimination between correct and shuffled pairs but did not establish the smoothness assumption.

Ablations add nuance: directly following the field at prediction time slightly outperformed FlowAlign on PBMC pair-retrieval metrics, but preserved cell-type structure less well. FlowAlign also cost more to train—about 5.5 versus 2.1 minutes on PBMC, excluding preprocessing and evaluation.

The method requires paired data, compatible vector representations and a well-learned field. It cannot guarantee retention of source-specific information absent from the target. Three-run single-cell variability estimates used a fixed data split, so they do not measure sensitivity to alternative splits. The preprint supports a promising alignment strategy within the tested settings, rather than a universal solution.