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MRFlow: Mechanism-Structured Residual Flow Matching for Virtual Cell Perturbation Prediction

Haojie Yang, Ran Su

arXiv:2610.13966v1cs.LGcs.AIq-bio.QM

TL;DR

Single-cell perturbation predictors often reduce conditions to mean expression shifts, despite meaningful variation among cells. MRFlow transports control populations through structured conditional latent dynamics and achieves the highest composite score across eight benchmarks.

  • Problem

    Many perturbation predictors target condition-level mean shifts, although responses include rare states, resistant subpopulations, and cell-state-dependent effects.

    Source: §1 · p. 2

  • Method

    MRFlow uses OT-guided conditional flow matching in a variational latent space, with a shared-operator affine field, low-rank correction, residual field, and count-aware decoding.

    Source: §1 · p. 2

  • Results

    MRFlow obtains the highest composite score across eight human single-cell perturbation datasets covering genetic and drug interventions.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The results support evaluating virtual cells as population generators using differential-expression accuracy, population distance, and response-gene consistency, rather than only mean-response regression.

    Source: §5 · p. 9

    Evaluation is per dataset rather than jointly trained across datasets; broader dose programs, perturbation modalities, and experimental validation remain future directions.

    Source: §2 · p. 30

Abstract

from arXiv · show

Predicting cellular responses to chemical and genetic perturbations is a central test for AI virtual cells, yet many single-cell models reduce each condition to an average expression shift. This target is misaligned with perturbation biology: rare states, resistant subpopulations, and context-dependent effect sizes may coexist under the same intervention. MRFlow treats virtual-cell prediction as conditional transport between empirical single-cell measures. Control and perturbed cells are embedded in a variational latent state space, greedy low-cost supervision is constructed over detached minibatch states, and a conditional flow-matching vector field transports control populations toward perturbed populations. The field decomposes into a mechanism-structured affine dictionary, which recombines shared latent response operators with a low-rank condition-specific correction, and a spectrally controlled residual field for nonlinear cell-level variation. Genetic perturbations are encoded through a regulatory-graph GCN, chemical perturbations through Morgan fingerprints, and both enter the same conditional dynamics interface. Across eight gene and drug perturbation benchmarks, MRFlow attains the highest composite score while preserving competitive raw performance on differential-expression and distributional metrics. The results support latent distribution transport as a principled and empirically effective formulation for perturbation-aware virtual cell modeling.

1 Introduction

Single-cell perturbation prediction must capture response distributions, not only condition-level mean shifts. MRFlow models these responses as conditional latent transport and achieves the highest composite score across eight datasets.

1 Introduction

  • Mean-shift predictions miss rare transcriptional states, resistant subpopulations, and cell-state-dependent effect sizes; benchmark rankings also vary with baselines and evaluation context.Source: §1 · p. 2
  • Standard flow models do not by themselves address unpaired perturbation measurements or structured extrapolation across conditions.Source: §1 · p. 2
  • MRFlow transports control-cell distributions toward perturbed-cell distributions using shared response operators, low-rank condition-specific corrections, and a spectrally regularized residual field.Genetic and chemical perturbations use modality-specific encoders but parameterize the same latent dynamics.Source: §1 · p. 2
  • MRFlow obtains the highest composite score across eight human single-cell perturbation datasets spanning genetic and drug screens.Ablations attribute performance to the structured affine field, residual field, low-rank correction, OT-guided pairing, and count-aware training.Source: §1 · p. 2

2 Related Work

Related work spans conditional perturbation predictors, transcriptomic foundation models, flow matching and optimal transport, and count-aware generative models. MRFlow combines conditional transport with structured dynamics and modality-specific encoders.

2.1 Single-cell perturbation prediction

  • Computational models built on these data include scGen, CPA, GEARS, and GenePert; benchmark studies stress that split design and systematic variation materially affect generalization conclusions.Source: §2.1 · p. 3

2.2 Single-cell foundation models

  • Transcriptomic foundation models offer broad representations, but representation scale does not automatically yield stronger held-out perturbation prediction.The passage describes MRFlow as complementary because it directly models the perturbation response operator and constrains conditional dynamics.Source: §2.2 · p. 3

2.3 Flow matching and optimal transport

  • Flow matching trains continuous dynamics without repeated likelihood-based ODE objectives, and minibatch optimal transport couples source and target samples through low-cost assignments.MRFlow adapts these approaches to latent prediction with unpaired measurements and held-out conditions.Source: §2.3 · p. 3

2.4 Generative count models and perturbation encoders

  • Count-aware generative models commonly use negative binomial likelihoods; MRFlow combines this decoder with transport and routes gene and drug encoders into one shared dynamics field.Genetic interventions use graph information, while chemical interventions use molecular fingerprints.Source: §2.4 · p. 3

3 Method

MRFlow encodes control and perturbed cells in a latent state space, learns conditional population transport from low-cost minibatch pairings, and decodes predictions as count-aware expression distributions. Structured affine dynamics, residual corrections, and modality-specific encoders define the transport model.

3.1 Virtual cell prediction as latent distribution transport

  • The prediction target is a perturbed-cell population distribution in latent space, with variational encoding mapping expression profiles to latent states.At inference, the encoder uses the posterior mean as the latent state.Source: §3.1 · p. 4

3.2 OT-guided latent flow matching for unpaired data

  • For unpaired populations, MRFlow recomputes greedy nearest-neighbor pairings over detached minibatch states, supplying transport-guided supervision without claiming exact global optimal transport.The model learns a conditional vector field along interpolated paired endpoints.Source: §3.2 · p. 4

3.3 Mechanism-structured residual vector field

  • The velocity field adds a nonlinear residual to a dominant affine trend, whose condition-specific matrix recombines shared response operators with a low-rank correction.Spectral normalization and a residual norm penalty constrain nonlinear corrections, which model cell-level variation beyond the affine component.Source: §3.3 · p. 5

3.4 Perturbation-conditioned encoding

  • Genetic perturbations use a regulatory-graph convolutional encoder, while drug identities use Morgan fingerprints; both modalities feed a shared condition interface.Dose and cell context also contribute to the fused condition embedding.Source: §3.4 · p. 5

3.5 Count-aware decoding and full objective

  • A negative binomial decoder models gene proportions and dispersion, while training combines flow matching, count reconstruction, variational regularization, structured-field penalties, and auxiliary entropic OT alignment.Source: §3.5 · pp. 5–6

3.6 Inference

  • Inference starts from control-cell latent states, integrates the learned conditional ODE, and decodes predicted endpoints into expression space for evaluation.Source: §3.6 · p. 6

4 Experiments

Across eight genetic and drug perturbation benchmarks, MRFlow ranks first by composite score, with raw metrics supporting the ranking. The experiments also test component contributions and inspect the learned transport dynamics.

4.1 Datasets, baselines, and metrics

  • Four genetic and four drug benchmarks contain 1.50 million profiles and 2,121 conditions, evaluated with matched condition-level splits and four metrics.The compared methods include statistical baselines, conditional autoencoders, graph and chemical-response models, gene-embedding linear models, and scGPT.Source: §4.1 · p. 6

4.2 Main results

  • MRFlow ranks first by composite score on all eight benchmarks, with raw metrics supporting the ranking.Tables 1 and 2 report the drug and genetic held-out-condition metrics.Source: §4.2 · p. 6, Table 1 · p. 7, Table 2 · p. 7

4.3 Ablations

  • On SciPlex3, K = 16 improves all metrics over K = 1, while K = 32 adds no gain; removing the macro field drops DE20 Pearson from 0.9608 to 0.6595.Removing the residual field also degrades performance, and random pairing increases E-distance from 9.9167 to 17.0063; these ablations use SciPlex3.Source: §4.3 · pp. 7–8

4.4 Interpretability and dynamics

  • On SciPlex3 pathway groups, the macro field contributes 51.5%–52.7% of predicted velocity, while 92%–94% of operator eigenvalue modes remain inside the unit circle.The few outside modes are interpreted as drug-specific strong-response directions; the HDAC inhibitor examples check downstream-marker response geometry, not recovery of the HDAC regulatory program.Source: §4.4 · pp. 8–9, Figure 4 · p. 8

5 Conclusion

MRFlow formulates perturbation prediction as conditional latent distribution transport, combining structured and residual dynamics with count-aware decoding. Across eight benchmarks, the results support evaluating virtual cells as population generators, while the model remains trained per task.

5 Conclusion

  • MRFlow combines OT-guided flow matching, a mechanism-structured affine dictionary, residual correction, and count-aware decoding for conditional latent distribution transport.The affine dictionary recombines shared latent response operators with a low-rank condition-specific correction.Source: §5 · p. 9
  • Across eight benchmarks, raw metrics and ablations support evaluating virtual cells as population generators rather than only mean-response regressors.Source: §5 · p. 9
  • MRFlow is a task-level architecture trained per benchmark, offering a route to evaluation by differential-expression accuracy, population distance, and response-gene consistency.Source: §5 · p. 9

A Raw Metrics Across Benchmarks

The raw-metric comparisons show both cross-benchmark strengths and metric-specific trade-offs. The composite score aggregates four metrics after per-dataset normalization, so it summarizes relative performance rather than absolute biological distance.

A Raw Metrics Across Benchmarks

  • The raw comparisons separate mean-effect accuracy, measured by DE20 Pearson and MSE, from population-level agreement, measured by Wasserstein distance and E-distance.Drug and genetic benchmark visualizations complement the tables rather than replacing the raw metrics.Source: A Raw Metrics Across Benchmarks · p. 14, Figure A.1 · p. 14, Figure A.2 · p. 15
  • MRFlow has the strongest DE20 Pearson, DE20 MSE, and E-distance on SciPlex3, while drug benchmarks also show metric-specific trade-offs.The broader drug comparison retains MRFlow's best aggregate ranking, but individual baselines remain competitive on single metrics; Aissa has only three non-control drug conditions.Source: A Raw Metrics Across Benchmarks · pp. 14–15, Figure A.1 · p. 14
  • MRFlow has the best composite score on Adamson, Dixit, Norman, and Replogle while preserving competitive DE20 Pearson; on Replogle, GenePert has slightly higher Pearson but MRFlow has lower Wasserstein and E-distance.Source: A Raw Metrics Across Benchmarks · p. 15, Figure A.2 · p. 15

B Composite Score Definition

  • The composite score equally averages four metrics normalized independently within each dataset, making it a relative benchmark summary rather than an absolute biological distance.Source: B Composite Score Definition · pp. 15–16

C Dataset and Split Details

The evaluation holds out perturbation conditions, with condition identity incorporating dose and cell context when annotated. Dataset-specific control designs and the small Aissa condition set qualify interpretation of the results.

C Dataset and Split Details

  • The held-out unit is a perturbation condition, defined by perturbation identity and, when present, dose and cell context; random condition splits use a 0.2 test ratio.This is not a strictly unseen-gene-identity or unseen-drug-identity split.Source: C Dataset and Split Details · pp. 16–17
  • The eight benchmarks cover genetic CRISPRa, CRISPRi, and knockout screens and chemical screens spanning cell lines, doses, resistance-associated response, and combinations.Source: C Dataset and Split Details · p. 16
  • Replogle uses non-targeting sgRNA as an internal control, while Aissa has only three non-control drug conditions, making its aggregate statistics more sensitive to individual conditions.Source: C Dataset and Split Details · p. 16, Table C.1 · p. 17
  • Methods share the processed expression matrix and held-out conditions within each dataset, so comparisons use matched inputs and evaluation partitions.Source: C Dataset and Split Details · p. 17

D OT-Guided Pairing Implementation

MRFlow constructs flow-matching supervision by pairing control and perturbed cells within each condition using low-cost latent matches. The pairing is a recomputed, non-differentiated training assignment, not a claim of biological ancestry.

D OT-Guided Pairing Implementation

  • Greedy nearest-neighbor low-cost pairing matches control states to nearby perturbed endpoints within each condition to provide coherent local velocity targets.The assignment is recomputed per minibatch and does not imply that a control cell is the biological ancestor of a perturbed cell.Source: D OT-Guided Pairing Implementation · p. 17
  • Detached latent states define the pairing cost, while gradients flow through the flow-matching loss and differentiable model computations.Detaching prevents the encoder from changing the pairing geometry to reduce assignment cost.Source: D OT-Guided Pairing Implementation · p. 17
  • Random endpoint pairing preserves relatively high DE20 Pearson but substantially worsens E-distance, indicating a larger effect on population geometry than mean-response correlation.The auxiliary endpoint-alignment term is entropic OT, distinct from a debiased Sinkhorn divergence.Source: D OT-Guided Pairing Implementation · p. 18

E Training Objective and Stabilization

MRFlow combines flow matching with count-aware reconstruction, latent-space regularization, and structured-field constraints. The objective also incorporates endpoint alignment and training stabilizers for condition-specific response genes and imbalanced conditions.

E Training Objective and Stabilization

  • The objective combines flow matching with negative-binomial reconstruction, KL regularization, structured-field penalties, and auxiliary entropic OT endpoint alignment.These terms address distinct training concerns: transport, count-aware expression, latent regularization, field magnitude, and predicted-to-target population alignment.Source: E Training Objective and Stabilization · p. 18
  • Negative-binomial reconstruction keeps latent states tied to count-aware expression distributions for control and perturbed cells.Differentially expressed genes receive condition-specific upweighting during reconstruction.Source: E Training Objective and Stabilization · pp. 18–19
  • KL warmup and free-bits-style stabilization limit very small per-dimension KL contributions that can contribute to posterior-collapse behavior.Condition-balanced sampling gives higher probability to conditions with fewer cells so large conditions do not dominate updates.Source: E Training Objective and Stabilization · pp. 18–19
  • The objective is a practical coupled training principle, not a theorem that each term uniquely identifies a biological mechanism.SciPlex3 ablations show distinct degradation patterns, but do not prove causal necessity in every dataset.Source: E Training Objective and Stabilization · pp. 18–19

F Baseline and Preprocessing Details

Baseline comparisons use shared held-out conditions, processed expression inputs, gene vocabulary, and metric computation. The study reports single-run results without seed-level confidence intervals and describes compute requirements and intended uses alongside cautions about in-silico predictions.

F Baseline and Preprocessing Details

  • Every method uses the same held-out perturbation split, processed expression matrix, benchmark gene vocabulary, and metric pipeline within each dataset.This input alignment is important for distributional metrics that can vary with preprocessing, vocabulary, and cell subsampling.Source: F Baseline and Preprocessing Details · p. 19
  • The baseline set spans population-summary and simple-regression baselines alongside learned perturbation models with differing condition encodings, graph use, chemical handling, and pretraining.The comparison is designed to test performance beyond weak baselines and a single model family.Source: F Baseline and Preprocessing Details · p. 19
  • The benchmark reports a single-run comparison and no confidence intervals across random seeds, leaving seed-level uncertainty outside its claims.The shared split and metric computation remain consistent across methods.Source: F Baseline and Preprocessing Details · p. 20

G Compute Resources and Broader Impact

  • Experiments used one RTX 5090 GPU and took approximately 3 to 8 hours per dataset; predictions are proposed for prioritization before wet-lab validation, not as clinical or causal evidence.The paper cautions that predictions may reflect training-atlas, preprocessing, or benchmark-split biases.Source: G Compute Resources and Broader Impact · p. 20

H Additional Quantitative Evidence

Raw-metric ranks show MRFlow near the top across both drug and genetic benchmarks, while SciPlex3 ablations link distinct model components to different metric changes. The dictionary-capacity sweep supports a bounded expressivity–regularization trade-off rather than an assumption that more bases always improve results.

H Additional Quantitative Evidence

  • Drug tasks rank MRFlow first in 10 of 16 dataset-metric cells and top two in 13 of 16, while genetic tasks rank it first in 12 of 16 and top two in 15 of 16.The corresponding mean ranks are 2.0625 for drug tasks and 1.3125 for genetic tasks; these are raw-metric rank summaries, not significance tests.Source: Figure H.2 · p. 21, H Additional Quantitative Evidence · p. 21
  • On SciPlex3, removing the macro field most damages DE20 correlation, whereas random pairing mainly increases distributional error, including E-distance.Other ablations affect different parts of the metric profile, consistent with distinct component roles.Source: Figure H.3 · p. 22, H Additional Quantitative Evidence · p. 22
  • On SciPlex3, increasing shared dictionary bases from K = 1 to K = 16 improves Pearson, MSE, and E-distance, while K = 32 gives no further gain.The sweep supports a structured expressivity–regularization trade-off rather than a claim that more bases always improve performance.Source: H Additional Quantitative Evidence · p. 23, Figure H.4 · p. 23

I Supplementary Tables for Mechanism-Structured Diagnostics and Example Provenance

The supplementary diagnostics examine whether MRFlow’s shared operators organize perturbations consistently with pathway annotations and how its affine and residual fields contribute. Selected dose-response and gene-shift panels provide local examples, while the benchmark tables remain the primary evidence for overall performance.

I Supplementary Tables for Mechanism-Structured Diagnostics and Example Provenance

  • Annotated same-class perturbations show higher α-space similarity than different-class perturbations, and nearest-neighbor enrichment exceeds permutation nulls.The level-2 pathway result is stronger than the level-1 result, while some MoA classes show negative differences; the evidence supports pathway-consistent operator organization, not one-to-one pathway mapping.Source: I Supplementary Tables for… · pp. 23–24, Table I.1 · p. 24, Table I.2 · p. 24
  • Pathway groups recruit different combinations of the 16 shared affine bases, with broad groups showing smaller mean activations than some specialized groups.The signs describe latent operators, not direct gene activation or repression.Source: I Supplementary Tables for… · p. 24, Table I.4 · p. 25
  • The macro field contributes slightly more than half across pathway groups, while residual norms remain substantial.This matches the intended division between reusable affine response and nonlinear, cell-state-dependent variation.Source: I Supplementary Tables for… · p. 25, Table I.5 · p. 25
  • Selected four-dose series show high predicted–observed rank agreement in several cases, but candidate series also include weak or negative agreement.Measured and predicted amplitude ranges differ, and the selected series are diagnostics rather than a global dose-response benchmark.Source: I Supplementary Tables for… · pp. 25–26, Table I.7 · p. 26, Table I.6 · p. 26
  • In the displayed case, the largest operator component is the bias term, followed by shared bases, while the low-rank correction contributes a small fraction.All displayed genes preserve the down-regulated direction, though absolute errors vary by gene; this case is not a substitute for aggregate benchmarks.Source: I Supplementary Tables for… · p. 27, Table I.10 · p. 27, Table I.11 · p. 28

J Supplementary Matched Response-Gene Shift Examples

  • Selected response-gene panels are high-matching examples, not unbiased estimates of global performance; Aissa PC9 contributes three real conditions because only three non-control conditions were available.The selection favors direction agreement, visible response magnitude, and low absolute error; the panels show locally inspectable signatures rather than replacing aggregate metrics.Source: I Supplementary Tables for… · p. 26, Table I.8 · p. 27, Table I.9 · p. 27

2. Limitations

  • The paper bounds its claims to held-out-condition prediction on reported benchmarks, and presents a model contribution rather than formal theorems; it reports experimental details and raw-metric diagnostics.The evaluation is described as per-dataset rather than jointly trained across datasets.Source: §2 · p. 30, §1 · p. 30, §3 · p. 30

5. Open access to data and code

  • The current submission lacks an attached code and reproduction package, does not list every dataset and software license individually, and reports no new human-subject experiments.The authors describe a planned public code release upon acceptance and potential benefits and risks of perturbation prioritization and drug-response analysis.Source: §5 · p. 30, §12 · p. 31, §13 · p. 31
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