FACET: Factorized Asymmetric Conditioning for Efficient Transport in High-Fidelity Fluorescence Microscopy Synthesis

• Cellular context is spatially aligned with the target, whereas sequence is non-spatial and specifies protein-dependent localization within that context.Localization also spans recurring patterns shared across proteins and finer protein-specific variation.Source: §1 · p. 1
• FACET factorizes sequence semantics into shared coarse patterns retrieved from a context-residualized memory and bounded protein-specific variation for conditioning stochastic transport.The framework is designed to learn sequence semantics from what context leaves unexplained and favor generalization to unseen proteins.Source: §1 · pp. 1–2
• 34.3% and 14.0% higher spatial overlap on HPA and OpenCell, respectively, and 27.2% and 46.5% lower FID, with 75% fewer network evaluations than a backbone-matched baseline.Source: §1 · p. 2
• The contributions include a latent-variable formulation with blockwise training and an exact variance-preserving state projection, with under 0.6% parameter overhead.Controlled ablations examine semantic, hierarchical, and transport components; further analyses report cross-dataset transfer, gains across multi-channel context compositions, protein-association recovery, and calibration.Source: §1 · p. 2
• Earlier sequence-conditioned localization models mainly advance image models; FACET instead factorizes sequence semantics and cellular context within a conditional generator.The authors compare in a backbone-matched setting and describe FACET as complementary to pretrained variance-preserving backbones.Source: §1 · p. 2

2.1 FACTORIZED PROBABILISTIC MODEL

• The conditional latent model separates shared prototype selection, continuous sequence-specific residual variation, and image transport while retaining direct conditioning on sequence and context.Context supplies spatial organization, prototypes supply coarse sequence semantics, residuals capture finer variation, and the image model captures realization-level variation.Source: §2.1 · pp. 2–3

2.2 CONTEXT-RESIDUALIZED SEMANTIC MEMORY

• A context predictor is subtracted from target features to form residuals, which are projected into protein-level representations and grouped into frozen, annotation-derived prototype centroids.At inference, a sequence prior provides a soft memory readout over those prototypes without discrete sampling noise.Source: §2.2 · p. 3

2.3 BOUNDED VARIATIONAL SEQUENCE RESIDUAL

• The sequence residual captures variation beyond the coarse memory readout, with posterior and prior means bounded relative to the empirical coarse-memory scale.The fixed covariance prevents reducing divergence by inflating a learned variance.Source: §2.3 · pp. 3–4

2.4.1 VARIANCE-PRESERVING STOCHASTIC INTERPOLANT

• A stochastic interpolant connects a noise latent to the target latent, and variance-preserving normalization lets a pretrained finite-schedule ε-predictor drive continuous stochastic transport.The state projection is exact; only the finite-schedule lookup is approximate, and the projection folds both noise sources into a single effective noise.Source: §2.4.1 · p. 4

2.4.2 CONTEXT-FIRST HIERARCHICAL CORRECTION

• The hierarchical correction refines features after they absorb cellular context, using sequence-conditioned modulation and a gated velocity correction alongside the pretrained predictor’s direct sequence pathway.Source: §2.4.2 · pp. 4–5

2.5 TRAINING AND INFERENCE

• Training proceeds in stages, establishing context-residualized memory and the prototype prior before optimizing the continuous residual and conditional transport components.The transport objective uses flow matching as a likelihood surrogate, a residual KL term, a prototype KL term, and auxiliary regularizers; inference integrates the resulting SDE and decodes the final latent.Source: §2.5 · p. 5

3.2.1 RESULTS ON HPA

• FACET achieves the best value on all six reported HPA image-quality metrics with 25 network evaluations per image versus 100 for CELL-Diff; IoUcont rises from 0.2478 to 0.3328 and FID falls from 45.6 to 33.20.Generation time for the 696-image test set falls from 78 to 15 minutes on the same GPU.Source: Table 1 · p. 6, §3.2.1 · p. 7

3.2.2 PERFORMANCE ACROSS CELLULAR-CONTEXT COMPOSITIONS

• Across HPA context compositions, FACET improves every reported metric in partial multi-channel and full-context regimes; with nucleus-only context, it retains gains in IoUcont and Haralick agreement, while CELL-Diff leads on the other reported metrics.Withheld channels use the pretrained predictor’s placeholder embedding in both context representations, giving each system the same ablated context.Source: Table 2 · p. 6, §3.2.2 · p. 7

3.3 CROSS-DATASET EVALUATION

• On OpenCell, HPA-module transfer improves MI slightly, Haralick agreement, PSNR, IoUcont, and FID over CELL-Diff, while OpenCell adaptation improves most reported metrics over transfer, with a small PSNR decrease.Both comparisons use nucleus-only context and the OpenCell CELL-Diff checkpoint backbone.Source: Table 3 · p. 7, §3.3 · p. 7

3.4 SPATIALLY RESOLVED PROTEIN-ASSOCIATION PATTERN RECOVERY

• FACET yields larger positive separation than CELL-Diff at all four STRING thresholds; at scores ≥0.85, Δ rises from +0.1005 to +0.1875, and at ≥0.40, from +0.0925 to +0.1289.All four FACET contrasts are significant by two-sided Mann-Whitney U tests, with p values from 1.7 × 10^-5 to 1.3 × 10^-3.Source: Table 4 · p. 7, §3.4 · p. 8

3.5.1 PATHWAY ABLATION; 3.5.3 ABLATION ON ADAPTATION CONFIGURATIONS

• On HPA, adding the sequence-conditioned semantic pathway raises IoUcont from 0.2581 to 0.2826, while the complete configuration reaches 0.3328; on OpenCell, performance depends on initialization and memory refitting, with warm-start refitting nearly recovering cold-start overlap.The cold-start configuration with OpenCell-fitted memory gives the highest overlap, 0.4244.Source: Table 5 · p. 8, §3.5.1 · p. 8, Table 6 · p. 8

3.5.2 QUALITY-COST TRADE-OFF

• On OpenCell, FACET reaches FID 36.83 at 25 NFE versus CELL-Diff’s 68.90 at 100 NFE, reducing network evaluations per image by 75%.The comparison is summarized in Figure 3.Source: Figure 3 · p. 8, §3.5.2 · p. 8

3.5.4 ABLATION OF INFERENCE-TIME MEMORY

• On HPA, learned inference-time memory gives IoUcont 0.3328, compared with 0.2820 for the uniform prototype mean and 0.3014 for zero memory.The authors attribute zero memory’s smaller degradation to the centered standardized PCA space; the uniform mean overweights rare localization categories.Source: §3.5.4 · pp. 8–9, Table 7 · p. 9

3.5.5 SAMPLER ABLATION

• At matched NFE on OpenCell, Euler-Maruyama SDE and Heun probability-flow ODE samplers reach nearly identical FID, while the SDE sampler has slightly higher IoUcont.Both remain below CELL-Diff at 100 NFE (FID 68.90).Source: Table 8 · p. 9, §3.5.5 · p. 9

4 CONCLUSION

• On unseen proteins across two benchmarks, FACET improves spatial and distributional fidelity, protein-association recovery, and calibration, with gains attributed to factorization rather than generator capacity.The conclusion describes the approach as complementary to stronger backbones and a template for conditional generation when inputs differ in spatial alignment and explanatory power.Source: §4 · p. 9
• FACET inherits its backbone’s finite noise schedule, which bounds usable sampling steps; continuous-time variance-preserving backbones are identified as a way to lift this bound.Extending the method to 3D, time-lapse imaging, multi-protein generation, and perturbations is described as future work.Source: §4 · p. 9

A RELATED WORK

• Prior multimodal-fusion work studies discriminative imbalance, whereas FACET assigns conditions distinct but coupled roles in a generative setting.Related protein-image generators condition jointly on sequence and morphology; FACET focuses on structuring those inputs rather than introducing a new image backbone.Source: A RELATED WORK · p. 13

B.1 TRAINING OBJECTIVE AND CURRICULUM

• Training proceeds in stages: memory, context map, prototype prior, and ε-adapter are prepared first, followed by residual and transport training with a three-phase curriculum.The later phases introduce posterior residuals and then ramp toward prior-sampled residuals, matching inference use.Source: §B.1 · pp. 14–15

B.2 PROTOTYPE CONSTRUCTION DETAILS

• The semantic memory is built from context-residualized target features, with protein-level averaging and a 128-dimensional projection retaining 71.2% of explained variance.The memory contains nine annotation-derived prototypes, and its transformations and centroids are fitted on training proteins and frozen before evaluation.Source: §B.2 · p. 16

B.3 ARCHITECTURE AND IMPLEMENTATION DETAILS

• The reported model keeps the pretrained predictor, VAE, sequence encoder, fitted maps, projections, memory, prior, and ε-adapter frozen while training transport residuals, the context-first head, and LoRA.The deployed instantiation adds 9.83M trainable parameters, or 0.588% of its 1.67B parameters.Source: §B.3 · p. 16

B.4 TRANSPORT DISCRETIZATION AND INFERENCE

• The continuous interpolant is projected onto the pretrained variance-preserving family exactly, while selecting a represented native noise level remains an approximation.The lookup chooses a native level rather than a continuously adjustable predictor timestep.Source: §B.4 · p. 17
• The primary sampler uses 25 network evaluations over τ=0.05 to 1, and initializes from a noise-derived latent that approximates the target-dependent interpolant marginal.The deterministic ODE variant is evaluated only as a sampling ablation.Source: §B.4 · p. 17

B.3 ARCHITECTURE AND IMPLEMENTATION DETAILS

• FACET composes a memory-conditioned base velocity with a gated hierarchical correction, then integrates the result through stochastic transport before decoding with the frozen VAE.The context-first head conditions the correction on context and the derived semantic state.Source: §B.3 · p. 17, Figure 4 · p. 18

D.1 PROOF OF PROPOSITION 1

• Applying Jensen’s inequality to the factored generative and posterior log-ratio yields a lower bound on the conditional latent likelihood.The ratio separates the image-latent likelihood, prototype prior and posterior, and protein-specific residual prior and posterior.Source: §D.1 · p. 18
• Training first constructs and freezes the memory and context map, pretrains the prototype prior and ε-adapter, then trains residual and transport components in phases.The curriculum progresses from the prototype state alone to posterior residuals and then prior residuals.Source: §D.1 · p. 19
• At inference, FACET obtains sequence and context representations, forms a soft memory readout and semantic state, then integrates a corrected velocity with Euler–Maruyama before decoding.The deployed semantic residual defaults to its prior mean, with predictive sampling available as an option.Source: §D.1 · p. 20

D.2 DERIVATION OF THE BASE LATENT ESTIMATE AND VELOCITY

• Under the stated Gaussian noise assumptions, conditional expectations yield the flow-matching target, while substituting predictor estimates gives the base velocity and a clean-latent estimate.The variance-preserving projection matches the predictor’s noise family, but nearest-index lookup approximates its finite schedule and the predicted noise estimates conditional rather than realized noise.Source: §D.2 · p. 21

D.3 DERIVATION AND INTERPRETATION OF THE AUXILIARY LATENT ESTIMATE

• An auxiliary training-time latent estimate assigns the velocity correction to the clean-latent component while retaining the adapted noise estimate, providing direct latent- and pixel-space supervision.This fixed-noise decomposition is a modeling choice, not a unique inversion of the corrected velocity.Source: §D.3 · p. 22

D.4 DERIVATION OF THE STOCHASTIC SAMPLER

• FACET combines its learned corrected velocity and approximate score in an SDE, sampled with Euler–Maruyama under the stochastic-interpolant framework’s stated conditions.The corresponding marginals require exact probability-flow velocity and score, along with initialization and regularity conditions.Source: §D.4 · p. 23

D.5 FIXED-SCALE KULLBACK–LEIBLER DIVERGENCE

• With shared isotropic covariance, the KL divergence between the residual Gaussians reduces to a squared distance between their means scaled by 1/(2σ_z^2).The derivation identifies this as the remaining quadratic term.Source: §D.5 · p. 23

D.6 PROOF OF PROPOSITION 2

• The final step of Proposition 2 uses the independence of z0 and ξ as standard Gaussian variables.The passage states that this independence proves the proposition.Source: §D.6 · p. 23

• HPA examples pair amino-acid sequences and target fluorescence images with nucleus, endoplasmic-reticulum, and microtubule context channels.Images are resized to 256 × 256 pixels before a frozen VAE maps them to 4 × 64 × 64 latent representations.Source: §E.1 · p. 24
• Sequence-length filtering yields an evaluation set of 696 images from 97 held-out proteins.The released test split's 720 images from 100 proteins is reduced by 24 images from three proteins at the 2048-token limit.Source: §E.1 · p. 24
• FACET adaptation and semantic-memory construction use 24,001 images from 3,491 training proteins, while the pretrained backbone uses the full training split.A protein-disjoint validation set of 349 proteins and 2,467 images is reserved for hyperparameter tuning and does not overlap the test proteins.Source: §E.1 · p. 24
• HPA evaluation compares four context-channel compositions: nucleus, nucleus+ER, nucleus+MT, and nucleus+ER+MT.Source: §E.1 · p. 24

E.2 OPENCELL BENCHMARK

• OpenCell's length-filtered test set contains 454 images from 97 proteins, and its adaptation split contains 5,659 images from 1,179 proteins.The released test set's 473 examples from 100 proteins is reduced by 19 examples; 10% of the adaptation proteins and corresponding images form validation.Source: §E.2 · p. 24
• OpenCell uses nucleus-only context and evaluates both HPA-module transfer and further adaptation on OpenCell training data.OpenCell test proteins are disjoint from the HPA training split used to fit the semantic memory.Source: §E.2 · p. 24

E.3 BACKBONE-MATCHED INSTANTIATION

• FACET and CELL-Diff share dataset-specific pretrained ε-predictor, VAE, and ESM-2 components, controlling comparisons for backbone capacity and pretraining.The CELL-Diff baseline uses the corresponding checkpoint without modification; this shared initialization is an experimental design choice, not part of FACET itself.Source: §E.3 · p. 25
• The evaluated FACET instantiation adds 9.83M deployed trainable parameters, or 0.588% of its 1.67B parameters.The reported module depths, LoRA rank, adapted projections, and optimization and sampling constants are implementation choices, not claimed to be optimal.Source: §E.3 · p. 25

E.4 HARDWARE SPECIFICATIONS

• Experiments used eight CPU cores, 64 GB of system memory, and one NVIDIA L40S GPU with 48 GB of memory.Source: §E.4 · p. 25

F.1 IMAGE-QUALITY METRICS

• Image quality uses MI, MS-SSIM, Haralick texture agreement, corpus-level PSNR, IoUcont, and FID; IoUcont is threshold-free weighted Jaccard similarity.FID compares 2048-dimensional Inception-v3 pool3 feature distributions, with lower values indicating closer agreement; NFE counts learned-model evaluations during sampling.Source: §F.1 · pp. 25–26

F.2 PROTEIN-ASSOCIATION EVALUATION

• Protein-association separation compares within-cell Pearson similarity of STRING-associated pairs with localization-matched non-associated pairs, after removing shared per-cell morphology.Positive separation indicates stronger association-consistent spatial patterns; significance is assessed separately for each system with a two-sided Mann-Whitney U test.Source: §F.2 · p. 26

F.3 PREDICTIVE CALIBRATION METRICS

• Calibration is evaluated with ECE, MCE, and Brier score; lower ECE and MCE indicate smaller calibration gaps, while lower Brier score indicates better probabilistic forecasts.ECE compares empirical foreground frequency with mean predicted probability across fixed probability bins.Source: §F.3 · p. 27

G STATISTICAL AND SAMPLING PROTOCOL

• Methods are compared on identical held-out examples, sequences, context inputs, and target images, using the same preprocessing and aggregation unless specified otherwise.Source: G STATISTICAL AND SAMPLING PROTOCOL · p. 27

G.1 PREDICTIVE CALIBRATION PROTOCOL

• Calibration uses 16 predictive samples per FACET image and a foreground threshold determined on held-out validation proteins, with no calibration parameter estimated from test pixels or proteins.A separate 96-image, 81-protein validation subset generates the predictive grid; the threshold is fixed before test scoring, and temperature scaling is fit on validation forecasts.Source: §G.1 · pp. 27–28

• 75% fewer network function evaluations accompany an approximately 80.8% reduction in wall-clock time: about 15 minutes for FACET versus 78 minutes for the reference on 696 HPA images.NFE is the primary compute measure because context loading and other system operations may cause small run-to-run timing variations; wall-clock time is a hardware-specific complement.Source: §G.2 · p. 28

H.1 CONDITIONING SENSITIVITY

• Sensitivity was estimated with Hutchinson trace estimators on 20 images from 18 proteins and five timesteps.The raw ratio’s median is 28.0, but differing latent scales make it descriptive rather than scale-independent.Source: §H.1 · p. 28
• The median normalized sensitivity is 3.645 for zS versus 0.606 for zC, making sensitivity to zS approximately sixfold higher under the observed latent scales.The reported 10th–90th percentile ranges are [1.236, 9.638] for zS and [0.431, 1.157] for zC.Source: §H.1 · p. 28
• The diagnostic measures local operating sensitivity, not a causal benefit of FiLM ordering, because no reversed-order model was trained.It supports the narrower conclusion that the implemented protein and context pathways have distinct, measurable effects.Source: §H.1 · p. 28

H.2 SAMPLING AND SCHEDULE REPRESENTABILITY

• Sampling uses a fixed τ range of [0.05, 1], but the pretrained schedule supports at most 67 evaluations without boundary fallback.At NFE 67, τemit = 0.985821; at NFE 68, τemit = 0.986029, outside the native schedule’s range.Source: §H.2 · pp. 28–29

I ADDITIONAL QUALITATIVE RESULTS

• Additional qualitative figures complement the main-paper comparison using the same visualization conventions and method names.The supplied passage introduces the additional figures but does not report their outcomes.Source: I ADDITIONAL QUALITATIVE RESULTS · p. 29

J DISCLOSURE OF GENERATIVE AI USE

• Large language models were used only to polish the text, not for retrieval, discovery, or research ideation.Source: J DISCLOSURE OF GENERATIVE AI USE · p. 29

I.1 CELLULAR-CONTEXT ABLATION

• With protein sequence fixed, Figure 5 varies cellular-context channels to visualize changes in generated spatial phenotype.The figure is qualitative evidence, not a causal ablation beyond the main text’s quantitative comparison.Source: §I.1 · p. 29, Figure 5 · p. 30

I.2 SAME-PROTEIN GENERATION ACROSS DIFFERENT CONTEXTS

• Figure 6 shows the same protein sequence evaluated under distinct HPA cellular contexts.Holding sequence fixed makes context-conditioned changes in generated spatial phenotype visible.Source: §I.2 · p. 29, Figure 6 · p. 31

I.3 ADDITIONAL PROTEIN AND CONTEXT COMBINATIONS ON HPA

• Figure 7 broadens HPA qualitative coverage with combinations of different proteins and cellular contexts.These examples extend beyond the representative examples in the main paper.Source: §I.3 · p. 29, Figure 7 · p. 32

I.4 ADDITIONAL QUALITATIVE COMPARISON ON OPENCELL

• Figure 8 adds qualitative comparisons on OpenCell using the main results’ method names and visualization conventions.“CELL-Diff (fine-tuned)” is the OpenCell-fine-tuned checkpoint also reported in the main text and the source (Zheng & Huang, 2025).Source: §I.4 · p. 29, Figure 8 · p. 33

I.5 ADDITIONAL QUALITATIVE COMPARISON ON HPA

• Figure 9 adds HPA qualitative comparisons using the main comparison’s method ordering and visualization conventions.CELL-E2 uses nucleus-only context, whereas CELL-Diff and FACET use the full three-channel context.Source: §I.5 · p. 29, Figure 9 · p. 34