arxiv: 2603.22564 · v2 · submitted 2026-03-23 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data

Alexander Tong, Brett Phelan, Christine L. Chaffer, Dhananjay Bhaskar, Guillaume Huguet, Guy Wolf, Jo\~ao Felipe Rocha, Ke Xu, Mark Gerstein, Natalia Ivanova, Oluwadamilola Fasina, Smita Krishnaswamy, Xingzhi Sun, Yanlei Zhang

Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:12 UTC · model grok-4.3

classification 💻 cs.LG

keywords cellular trajectoriessingle-cell transcriptomicsspatial transcriptomicsneural stochastic differential equationsoptimal transportmanifold learningcell fate inferencetissue regeneration

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The pith

MIOFlow 2.0 infers cellular trajectories by modeling stochastic branching, population growth, and spatial niche influences in a shared latent space.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces MIOFlow 2.0 to recover continuous cell trajectories from discrete single-cell and spatial transcriptomics snapshots. Existing methods rely on deterministic paths that ignore random fate decisions, shifts in cell numbers, and local signaling environments. The new framework combines a geometry-preserving autoencoder with neural stochastic differential equations and unbalanced optimal transport to capture these features together. A sympathetic reader would care because accurate trajectory maps can identify transition points and niche signals that drive development, regeneration, or disease progression. Validation on synthetic data, embryoid body differentiation, and axolotl brain regeneration shows the approach improves path accuracy and highlights hidden drivers such as specific signaling niches.

Core claim

MIOFlow 2.0 learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models stochasticity and branching via Neural SDEs, non-conservative population changes with a learned growth-rate model initialized by unbalanced optimal transport, and environmental influence through a joint latent space that unifies gene expression with spatial features such as local cell type composition and signaling. The latent space is constructed by a PHATE-distance matching autoencoder so that trajectories respect the data's intrinsic geometry.

What carries the argument

Joint latent space from a PHATE-distance matching autoencoder combined with Neural Stochastic Differential Equations that incorporate learned growth rates for population dynamics and spatial features.

If this is right

Neural differential equation models for trajectories outperform simulation-free flow matching and other generative baselines on the tested datasets.
The framework identifies specific signaling niches as drivers of cellular transitions in spatially resolved data.
Unbalanced optimal transport initialization enables modeling of non-conservative population changes during differentiation.
A single latent space unifies single-cell and spatial transcriptomics to recover tissue-scale trajectories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the stochastic components prove reliable, the model could support in silico perturbation experiments to test how changes in niche signals alter cell fate probabilities.
The growth-rate module might be adapted to datasets that include explicit cell death or proliferation measurements for more quantitative population forecasts.
Joint modeling of spatial and expression features suggests the method could generalize to other modalities that combine molecular profiles with positional information.
Improved trajectory accuracy could help prioritize candidate regulatory genes or ligands for experimental validation in regeneration studies.

Load-bearing premise

The PHATE-distance matching autoencoder latent space accurately captures the data's intrinsic geometry and the neural differential equations faithfully represent the underlying stochastic biological processes.

What would settle it

Predicted trajectories from MIOFlow 2.0 show large mismatches with ground-truth paths on a new synthetic dataset engineered with known stochastic branching and spatial signaling, or the model fails to recover established signaling niches in the axolotl regeneration data.

Figures

Figures reproduced from arXiv: 2603.22564 by Alexander Tong, Brett Phelan, Christine L. Chaffer, Dhananjay Bhaskar, Guillaume Huguet, Guy Wolf, Jo\~ao Felipe Rocha, Ke Xu, Mark Gerstein, Natalia Ivanova, Oluwadamilola Fasina, Smita Krishnaswamy, Xingzhi Sun, Yanlei Zhang.

**Figure 1.** Figure 1: Overview of the MIOFlow model. A. We initialize with scRNA-seq data and spatial transcriptomics, then concatenate both feature sets into a jointly embedded latent space. Each data point in this latent space represents a cell embedding informed by its neighbors. B. The embedding serves as input to three networks: a proliferation network predicting the proliferation rate, and drift and diffusion networks com… view at source ↗

**Figure 2.** Figure 2: features Extraction for MIOFlow 2.0. A. Build the neighborhood graph using knn graph or Voronoi polygons B. Compute local cell type frequency from neighborhood. Colors indicate cell types. C. Compute ligand-receptors signalling strength from neighbors to target cell. D. Local Expression Niche: The mean PCA embedding vector of neighboring cells E. Concatenate cell features with their spatial neighbors infor… view at source ↗

**Figure 3.** Figure 3: Comparison of trajectory inference methods on synthetic SERGIO datasets. (Top) Trifurcation dataset with three terminal [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

**Figure 4.** Figure 4: We evaluate MIOFlow 2.0 across three simulated datasets designed to mimic key biological characteristics: branching, [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗

**Figure 5.** Figure 5: Gene and spatial feature embeddings colored by (A) cell type annotation, (B) pseudotime point. (C) NCAN:SDC3 ligand [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗

read the original abstract

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disease. A key challenge is inferring continuous trajectories from discrete snapshots. Biological complexity stems from stochastic cell fate decisions, temporal proliferation changes, and spatial environmental influences. Current methods often use deterministic interpolations treating cells in isolation, failing to capture the probabilistic branching, population shifts, and niche-dependent signaling driving real biological processes. We introduce Manifold Interpolating Optimal-Transport Flow (MIOFlow) 2.0. This framework learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models three core processes: (1) stochasticity and branching via Neural Stochastic Differential Equations; (2) non-conservative population changes using a learned growth-rate model initialized with unbalanced optimal transport; and (3) environmental influence through a joint latent space unifying gene expression with spatial features like local cell type composition and signaling. By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data's intrinsic geometry. Empirical comparisons show expressive trajectory learning via neural differential equations outperforms existing generative models, including simulation-free flow matching. Validated on synthetic datasets, embryoid body differentiation, and spatially resolved axolotl brain regeneration, MIOFlow 2.0 improves trajectory accuracy and reveals hidden drivers of cellular transitions, like specific signaling niches. MIOFlow 2.0 thus bridges single-cell and spatial transcriptomics to uncover tissue-scale trajectories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

MIOFlow 2.0 unifies PHATE manifold learning, neural SDEs, and unbalanced OT into one pipeline for stochastic trajectories with spatial context, but the latent space geometry claim lacks reported validation metrics.

read the letter

The main takeaway is that MIOFlow 2.0 builds a single framework that combines a PHATE-distance matching autoencoder for the latent space, unbalanced optimal transport to initialize learned growth rates for population shifts, and neural stochastic differential equations to capture branching and noise in cell trajectories. It also folds spatial features like local cell composition and signaling into the same embedding so the model can reflect environmental influences. This is a direct response to the limits of deterministic interpolation methods that ignore stochasticity, proliferation changes, and spatial niches. On the synthetic benchmarks, embryoid body data, and axolotl brain regeneration example, the approach reportedly recovers trajectories more accurately than flow matching baselines and surfaces candidate signaling drivers. The joint handling of those three biological factors in one model is the clearest advance over prior separate pieces of work. The soft spot is the central reliance on the autoencoder to produce a faithful representation of the data's intrinsic geometry. The abstract states that this embedding ensures trajectories respect that geometry, yet no geodesic preservation errors, manifold reconstruction scores, or ablations against PCA or UMAP are described. If the latent space distorts local or global structure, the neural SDE and growth-rate components will simply follow the distortion rather than recover the underlying processes. That makes the empirical gains harder to attribute cleanly to the new components. This paper is aimed at computational biologists who already work on trajectory inference and want to add stochasticity plus spatial context without stitching separate tools together. It is coherent enough on its own terms and grounded in concrete datasets that it deserves a serious referee, even though the methods section will need close attention on the embedding validation and sensitivity to the free parameters in the growth and SDE models.

Referee Report

2 major / 2 minor

Summary. The paper introduces MIOFlow 2.0, a unified framework that learns cellular trajectories from single-cell and spatial transcriptomics by embedding data in a PHATE-distance matching autoencoder latent space, modeling stochastic branching and dynamics via Neural SDEs, capturing non-conservative population changes with a growth-rate model initialized from unbalanced optimal transport, and incorporating environmental influences (e.g., local cell-type composition and signaling) in a joint latent space. It reports improved trajectory accuracy over flow-matching baselines on synthetic data, embryoid-body differentiation, and axolotl brain regeneration, while identifying signaling niches.

Significance. If the central claims hold after validation, the work would provide a principled way to jointly handle stochasticity, proliferation, and spatial context in trajectory inference, extending beyond deterministic or simulation-free methods and enabling discovery of niche-driven transitions across single-cell and spatial modalities.

major comments (2)

[Methods (latent-space construction) and Results (validation)] The central claim that trajectories respect intrinsic geometry rests on the PHATE-distance matching autoencoder producing a faithful latent representation, yet the manuscript provides no quantitative validation of geometry preservation (e.g., geodesic distance error, local neighborhood fidelity, or reconstruction metrics) nor ablations against PCA/UMAP on the synthetic or real datasets. Without these, downstream Neural SDE and unbalanced-OT components risk propagating embedding distortions rather than recovering true stochastic dynamics.
[Results (comparisons to baselines)] The empirical superiority over simulation-free flow matching is stated but not supported by load-bearing quantitative details: specific trajectory accuracy metrics (e.g., Wasserstein distance to ground truth, branching fidelity scores), ablation studies removing the growth-rate or spatial components, and statistical tests on the embryoid-body and axolotl datasets are absent or insufficiently reported.

minor comments (2)

[Methods] Notation for the Neural SDE drift and diffusion terms, as well as the precise initialization of the growth-rate model from unbalanced OT, should be made explicit with equations.
[Figures] Figure legends for trajectory visualizations should include quantitative error bars or distance metrics rather than qualitative overlays only.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We have revised the manuscript to address the concerns on latent space validation and quantitative comparisons, adding the requested metrics, ablations, and statistical analyses.

read point-by-point responses

Referee: [Methods (latent-space construction) and Results (validation)] The central claim that trajectories respect intrinsic geometry rests on the PHATE-distance matching autoencoder producing a faithful latent representation, yet the manuscript provides no quantitative validation of geometry preservation (e.g., geodesic distance error, local neighborhood fidelity, or reconstruction metrics) nor ablations against PCA/UMAP on the synthetic or real datasets. Without these, downstream Neural SDE and unbalanced-OT components risk propagating embedding distortions rather than recovering true stochastic dynamics.

Authors: We agree that explicit quantitative validation of geometry preservation is needed to support the claim. In the revised manuscript we add geodesic distance error, local neighborhood fidelity (trustworthiness and continuity), and reconstruction metrics for the PHATE-distance matching autoencoder. We also include direct ablations against PCA and UMAP embeddings on the synthetic, embryoid-body, and axolotl datasets, with new figures and tables demonstrating superior manifold preservation. These additions appear in the Methods (latent-space construction) and Results sections. revision: yes
Referee: [Results (comparisons to baselines)] The empirical superiority over simulation-free flow matching is stated but not supported by load-bearing quantitative details: specific trajectory accuracy metrics (e.g., Wasserstein distance to ground truth, branching fidelity scores), ablation studies removing the growth-rate or spatial components, and statistical tests on the embryoid-body and axolotl datasets are absent or insufficiently reported.

Authors: We thank the referee for highlighting this gap. The revised manuscript now reports Wasserstein distances to ground-truth trajectories on synthetic data, branching fidelity scores, and ablation results that isolate the growth-rate and spatial components. We further include statistical significance tests (paired t-tests with p-values) comparing MIOFlow 2.0 against baselines on both the embryoid-body and axolotl datasets. These quantitative results and ablations are presented in updated tables and figures in the Results section. revision: yes

Circularity Check

0 steps flagged

No circularity: method is an explicit construction from independent components

full rationale

The paper presents MIOFlow 2.0 as an integrated modeling framework that combines existing techniques (Neural SDEs for stochasticity, unbalanced OT for growth rates, PHATE-distance autoencoder for latent space, joint gene-spatial features). No derivation chain is claimed that reduces a 'prediction' or 'first-principles result' back to its own fitted inputs or self-citations by construction. The central statements ('ensures trajectories respect the data's intrinsic geometry', 'improves trajectory accuracy') are design choices and empirical claims, not self-referential reductions. External validation on synthetic and real datasets (embryoid body, axolotl) is described, making the work falsifiable outside any internal loop. No self-citation load-bearing, ansatz smuggling, or renaming of known results appears in the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The framework rests on several learned components and geometric assumptions whose independence from the target trajectories is not detailed in the abstract.

free parameters (2)

growth-rate model parameters
Learned growth-rate model initialized with unbalanced optimal transport to handle non-conservative population changes.
neural SDE parameters
Parameters of the neural stochastic differential equations that model stochasticity and branching.

axioms (1)

domain assumption PHATE embedding preserves the intrinsic manifold geometry of the transcriptomics data
Used to define the latent space in which trajectories are learned.

pith-pipeline@v0.9.0 · 5641 in / 1356 out tokens · 48359 ms · 2026-05-15T00:12:42.804583+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear
By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data's intrinsic geometry.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
We employ Neural Stochastic Differential Equations... dZ_t = b(Z_t,t;θ)dt + σ(Z_t,t;ϕ)dW_t

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