[ICML 2025] Distribution-Conditioned Transport: Mastering Any-to-Any Generalization in Scientific Data

TL;DR

Researchers from MIT and Harvard have unveiled Distribution-Conditioned Transport (DCT), a framework that allows AI models to "transport" samples between distributions they have never seen before. By embedding entire populations into a latent space, DCT solves the "sparse data" problem in biology, enabling models to predict how cells evolve or respond to drugs even when data is missing for specific patients or timepoints.

The "Orphan" Problem in Modern Science

In fields like single-cell genomics, we rarely have a complete picture. We might see a patient's blood cells at Day 1 (Source) and Day 10 (Target), but for thousands of other "orphan" clones, we only see a single snapshot.

Current SOTA methods like Meta Flow Matching (MFM) are "supervised"—they need explicit Source-Target pairs to learn the mapping. If you don't have the pair, the data is wasted. Furthermore, these models often struggle to generalize to a brand-new "Batch" or "Donor" they didn't see during training.

Methodology: Embedding the Manifold of Distributions

The genius of DCT lies in its distributionally-invariant encoder. Instead of treating a batch as a "label" (e.g., "Patient A"), DCT treats it as a point on a continuous mathematical manifold of all possible distributions.

1. The Encoder

The model uses a permutation-invariant architecture (Deep Sets/GNN) to ensure that the order of cells doesn't change the outcome. This encoder produces a Distribution Embedding ($z$) that captures the "essence" of the population.

2. Any-to-Any Transport

The transport map $\mathcal{T}$ is conditioned on both $z_{src}$ and $z_{tgt}$. This creates a universal mapping function: $\mathcal{T}(x_i|z_{src},z_{tgt})$ Because the latent space is continuous, the model can move a cell from distribution A to distribution B even if it has only ever seen A and C paired before.

Empirical Evidence: Breaking the Zero-Shot Barrier

Batch Effect Transfer

In scRNA-seq, "batch effects" (technical noise between experiments) are a nightmare. DCT was tested on 56 mice; it was asked to predict how cells from a "held-out" old mouse would look compared to young mice.

• Result: DCT outperformed industry standards like scVI and Harmony in zero-shot transport. It didn't just align the data; it accurately predicted the distribution shift.

Leveraging "Orphan Marginals"

In T-cell receptor sequences (COVID-19 data), most patients were only sampled once. DCT's Semi-Supervised mode allowed training on cross-patient samples (Day 1 of Patient A $\to$ Day 10 of Patient B).

• Impact: This improved forecasting accuracy by over 50% compared to models that threw away the orphan data.

Depth Perspective: Why does this work?

The paper proves through a Loss CLT (Central Limit Theorem) that training on minibatches of sample sets behaves like training on the true underlying populations in the large-sample limit.

By conditioning on the target embedding, the model becomes a "Distribution Regression" engine. The authors found that even simple linear interpolation in this latent $z$-space corresponds to meaningful physical transitions in the real cell space, such as the developmental path of a stem cell (see latent interpolants trace).

Limitations & Future Work

While DCT is powerful, it can occasionally underperform "specialized" models on IID (In-Distribution) data because it is trying to learn the entire metadistribution rather than memorizing specific pairs. Future work will likely look at dynamic weighting—tuning the model to prioritize local accuracy while maintaining global generalization.

Takeaway

DCT represents a shift from "Task-Specific AI" to "Context-Aware AI" in the biological sciences. It signifies that the most efficient way to model complex systems is to learn the geometric structure of the distributions themselves.

Source: Fishman et al., "Distribution-Conditioned Transport", arXiv (2025). Codebase: [Link provided in paper]