D²R²

Knock down a transcription factor and the cell does not change every gene at once. Its direct targets move first, their targets move next, and much of the profile a Perturb-seq experiment records is downstream consequence rather than direct effect. Perturbation predictors emit the whole expression vector in a single pass, or denoise all of it together, so that regulatory chain never appears in the model: no predicted gene informs any other, and the order in which responses resolve is left unmodeled.

D²R² (Discrete Diffusion with Regulation Reinforcement), from Zhejiang University and City University of Hong Kong, makes that order an explicit, learned part of the model. Expression values are binned into ordinal tokens, and a masked discrete diffusion model (MDDM) fills a fully masked profile in stages: tokens committed at one step are frozen and become context for the genes still masked. Which genes get committed next is decided by a Regulatory Policy Module (RPM), initialized to reproduce an ordering taken from a gene regulatory network inferred from unperturbed control cells with DeepSEM and ranked by PageRank, so upstream regulators are resolved before the genes they govern.

That prior is generic to the cell type rather than to the perturbation, so a second training stage freezes the generator and refines only the ordering policy with group-relative policy optimization (GRPO), rewarding orderings whose finished profile agrees with the observed perturbation effect. The generator is never retrained by this step, which is what lets the paper attribute the resulting gains to ordering alone. The acronym is shared with an unrelated 2024 tabular few-shot learning method and an NSF RNA-regulome program; neither is this model.

#Key Features

• Gene-wise progressive generation: A profile is built over 20 steps of 50 genes rather than in one shot, so early responses condition later ones.
• Regulatory prior as generation order: A control-derived GRN, ranked by PageRank, places influential upstream regulators first — the direction matters, and reversing it degrades every metric.
• Perturbation-specific ordering: GRPO turns the static cell-type prior into a policy that recomputes gene priorities at each step from the perturbation and the partially generated state.
• Ordinal expression tokens: Continuous values map to 50 equal-frequency bins, putting expression in a discrete space where masking and progressive unmasking are natural.
• An interpretable trajectory: Regulatory genes dominate early steps, and perturbation-specific transcription factors are promoted ahead of non-specific ones.

#Technical Details

The denoising predictor is a 12-layer non-causal Transformer with hidden dimension 768, 12 attention heads, SwiGLU intermediate dimension 3072, RMSNorm, and dropout 0.1, operating over a fixed 1,000 highly variable gene panel with 50 expression bins. It is conditioned on a control profile, the perturbation, and cellular covariates, and trained with an x₀-prediction objective on masked positions; RPM is then optimized with GRPO over four rollouts per group, and inference is deterministic Top-K unmasking from the fixed checkpoint. Evaluation follows the PerturBench protocol on two datasets: Norman19, a K562 Perturb-seq set of 287 conditions including 131 combinatorial ones, split to hold out unseen perturbation combinations; and VCC-H1, roughly 400,000 H1 embryonic stem cells across about 300 CRISPRi targets from the Virtual Cell Challenge. On Norman19, D²R² leads all five metrics — Pearson Δ 0.706, Cos. LogFC 0.724, Cos. LogFC Rank 0.024, Cos. PCA 0.703, Sym. KL 0.148 — against SAMS-VAE, Biolord, STATE, CellFlow, Squidiff and scDFM; on H1 it leads the three differential-expression metrics. The controlled ablation is the load-bearing result: with the generator and the 20-step budget held fixed, biological-prior ordering beats random ordering, confidence- and entropy-based heuristics do not reliably help, and reversing the prior falls below random.

#Applications

The immediate use is in-silico triage for functional genomics: ranking which single or combinatorial CRISPR perturbations are worth running, given control cells from the same line. Because generation is ordered, the trajectory is itself an analytical output: the genes RPM promotes for a given perturbation are enriched for its differentially expressed genes and for cell-cycle pathways, giving a bench scientist a hypothesis about regulatory propagation, not just a predicted vector.

#Impact

D²R² argues that generation order is a design axis in virtual-cell modeling, not an implementation detail, and it supports the claim with an ablation that changes nothing but the order. That framing is portable to any progressive generative model of expression, including diffusion-based peers such as PerturbDiff and scDiffusion. The scope is narrow, though: a checkpoint is tied to its 1,000-gene panel and fitted binning statistics, and token counts differ between Norman19 and H1, so a separate MDDM is trained per dataset and a third dataset means retraining. The GRPO reward also needs observed perturbed profiles, making it a training-time procedure rather than test-time adaptation. As of August 2026 the work is an unrefereed preprint with no released code or checkpoints.