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\begin{document}

\title{Mask-Ratio Controlled Diffusion for Evolutionary Enhancer Sequence Generation}

\titlerunning{Mask-Ratio Controlled Diffusion for Enhancer Generation}

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\maketitle

\begin{abstract}
Enhancer sequence design requires generating DNA that is not only syntactically valid but also functionally aligned with desired regulatory activity.
Autoregressive genomic language models provide a natural interface for sequence generation, yet they generate bases sequentially from a prefix and may drift into locally high-probability patterns, such as repetitive continuations.
In contrast, biological evolution rarely rewrites an entire genome from scratch; it explores sequence space through localized mutation, selection, and accumulation.
Motivated by this observation, we study a mask-ratio controlled discrete diffusion framework for enhancer generation, where generation proceeds by masking and recovering a controllable fraction of DNA bases under activity conditions.
The mask ratio acts as an explicit mutation budget: low ratios perform local edits around an existing enhancer, while high ratios approach de novo generation from a fully masked sequence.
Using the DeepSTARR enhancer activity benchmark, we compare autoregressive generation, bucket-conditioned autoregressive generation, and bucket-conditioned masked diffusion under a unified predictor-guided evaluation protocol.
We evaluate activity controllability, DNA validity, sequence diversity, distributional fidelity, diffusion pseudo-likelihood, and regulatory sequence grammar.
On the validation split, all evaluated generators produce valid DNA, but they exhibit sharply different failure modes.
Autoregressive baselines obtain higher predictor scores than diffusion, but collapse toward low-GC repetitive continuations with long homopolymers.
In contrast, conditioned masked diffusion preserves reference-like GC content, homopolymer length, and $k$-mer statistics while maintaining valid and unique generated sequences.

\keywords{Enhancer design \and Regulatory DNA generation \and Discrete diffusion \and Genomic foundation models \and Controllable generation}
\end{abstract}

\section{Introduction}

Enhancers are non-coding regulatory elements that modulate gene expression programs across cell types and developmental contexts.
Designing enhancer sequences with desired activity is a central problem in regulatory genomics and synthetic biology.
Recent sequence-to-activity models, such as DeepSTARR, demonstrate that enhancer activity can be predicted directly from DNA sequence and that such predictors can guide synthetic enhancer design~\cite{dealmeida2022deepstarr}.
At the same time, genomic foundation models make it increasingly feasible to generate candidate DNA sequences at scale.
The main challenge is no longer only whether a model can emit valid DNA, but whether it can generate sequences that are functionally controlled, diverse, and biologically plausible.

Most language-model-based DNA generators follow an autoregressive formulation: a model receives a prefix and samples the next token repeatedly.
This is convenient for sequence continuation, but it is an imperfect match for enhancer design.
Enhancers are fixed-length regulatory programs whose activity may depend on motifs, spacing, local grammar, and global sequence composition.
A left-to-right generator can over-commit to early choices and may collapse into repetitive continuations.
More importantly, autoregressive generation resembles writing an enhancer from scratch or extending a prefix, whereas biological sequence evolution more often proceeds through mutation of existing sequences.

We therefore ask whether enhancer generation can be formulated as a controlled mutation process.
Instead of generating every base sequentially, a masked discrete diffusion model corrupts a sequence by masking a subset of positions and learns to recover the original bases.
At sampling time, the mask ratio can be selected explicitly.
A low mask ratio corresponds to local mutation: most of the original enhancer remains fixed while a small fraction of bases is regenerated.
A high mask ratio corresponds to broader exploration.
A fully masked sequence recovers the usual de novo generation setting.
This provides a single mechanism that interpolates between editing, optimization, and generation.

In this paper, we present \methodname{}, a mask-ratio controlled diffusion framework for controllable enhancer generation.
We use activity bucket tokens to condition generation on low, middle, or high enhancer activity.
Our evaluation is predictor-guided: a separately trained DeepSTARR activity predictor serves as a functional oracle, while sequence statistics and motif analysis measure whether generated DNA remains close to natural regulatory sequences.
We compare our diffusion approach with unconditional and bucket-conditioned autoregressive baselines built from a genomic foundation model.

Our contributions are:
\begin{itemize}
    \item We formulate enhancer generation as mask-ratio controlled sequence mutation, bridging local editing and de novo generation.
    \item We implement a bucket-conditioned masked discrete diffusion baseline for DeepSTARR enhancer sequences.
    \item We propose a unified evaluation protocol covering predicted activity, target-bucket controllability, validity, diversity, nearest-reference distance, k-mer distribution, diffusion pseudo-likelihood, and regulatory motif grammar.
    \item We provide an empirical comparison against autoregressive genomic language model baselines.
\end{itemize}

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/fig_pipeline_overview.png}
\caption{Overview of the proposed enhancer generation and evaluation pipeline. DeepSTARR sequences are bucketed by activity, a predictor is trained as an evaluation oracle, autoregressive baselines are compared against mask-ratio controlled diffusion, and generated sequences are evaluated for predicted activity, controllability, sequence quality, distributional fidelity, and diffusion pseudo-likelihood.}
\label{fig:pipeline}
\end{figure}

\section{Related Work}

\paragraph{Enhancer activity prediction.}
DeepSTARR predicts enhancer activity from DNA sequence and enables de novo synthetic enhancer design~\cite{dealmeida2022deepstarr}.
Such sequence-to-activity models provide a practical in silico oracle for ranking candidate regulatory sequences before experimental validation.
Our work follows this predictor-guided design paradigm, but focuses on comparing generative mechanisms and conditioning strategies rather than only optimizing sequences against a fixed predictor.

\paragraph{Generative regulatory DNA design.}
Prior work has explored generative models for regulatory DNA, including deep generative design of expression-controlling sequences~\cite{zrimec2022expressiongan}, cell-type-directed synthetic enhancer design~\cite{taskiran2024celltypedirected}, and machine-guided cis-regulatory element design~\cite{gosai2024coda}.
These studies emphasize that synthetic regulatory DNA should be evaluated not only by predicted activity but also by biological grammar, specificity, and diversity.
We adopt this multi-objective view in our evaluation.

\paragraph{Controllable genomic language models.}
Autoregressive language models and reinforcement learning have recently been used for controllable DNA sequence design~\cite{su2025atgcgen,yang2025rldna}.
These methods provide flexible conditional sampling, but they can suffer from diversity loss, reward hacking, or local repetitive patterns.
Our work studies autoregressive models as baselines and contrasts them with masked diffusion, which allows partial sequence corruption and recovery rather than one-way continuation.

\paragraph{Discrete diffusion for biological sequences.}
Discrete diffusion models have been applied to regulatory DNA design with tunable activity~\cite{sarkar2024d3} and to broader biological sequence optimization through reward fine-tuning~\cite{wang2024drakes}.
DNA-Diffusion further demonstrates the potential of diffusion-based design for synthetic regulatory elements~\cite{dasilva2026dnadiffusion}.
Our method is inspired by this line of work but centers on a mask-ratio interpretation: the corruption level becomes a controllable mutation budget, enabling both local enhancer editing and de novo generation under the same model.

\section{Methods}

\subsection{Problem Formulation}

Let $x = (x_1,\ldots,x_L)$ denote a DNA enhancer sequence of length $L$, where $x_i \in \{A,C,G,T\}$.
Each sequence has a two-dimensional activity label $y=(y_0,y_1)$ in the DeepSTARR benchmark.
We define a scalar activity score $s(y)$ for bucket construction:
\begin{equation}
    s(y) = y_0 + y_1.
\end{equation}
Using the training split, we assign samples to low, middle, and high activity buckets by the 25th and 75th percentiles of $s(y)$.
The corresponding condition tokens are $\langle sp0\rangle$, $\langle sp1\rangle$, and $\langle sp2\rangle$.

The goal is to learn a conditional generator $p_\theta(x \mid c)$, where $c$ is an activity bucket.
For mutation-like generation, we additionally condition on a reference sequence $x^{ref}$ and a mask ratio $\rho \in [0,1]$.
The model generates a sequence by preserving unmasked positions and resampling masked positions.
When $\rho=1$, all positions are masked and the model performs de novo generation.
When $\rho$ is small, the model performs local mutation around the reference enhancer.

\subsection{Activity Predictor}

We train a sequence-to-activity predictor $f_\phi(x)$ using a genomic foundation model with a regression head.
The predictor maps DNA sequences to two activity dimensions:
\begin{equation}
    f_\phi(x) = (\hat{y}_0, \hat{y}_1).
\end{equation}
This predictor is used only for evaluation and candidate scoring, not for training the diffusion model in the current version.
Predictor quality is evaluated on the held-out test set using Pearson correlation, $R^2$, MAE, and MSE.
The trained predictor obtains overall Pearson 0.652, $R^2=0.417$, MAE 0.590, and MSE 0.605.

\subsection{Autoregressive Baselines}

We consider two autoregressive baselines.
The first is an unconditional fine-tuned generator trained on enhancer sequences.
The second prepends an activity bucket token to each training sequence and learns $p_\theta(x_t \mid c, x_{<t})$.
At evaluation time, a prefix of the enhancer sequence is provided and the model generates the continuation.
This baseline tests whether simple condition-token prompting is sufficient to control enhancer activity.

\subsection{Mask-Ratio Controlled Discrete Diffusion}

Our diffusion generator is based on a masked language modeling objective.
For each training sequence, we sample a diffusion step $t \in \{1,\ldots,T\}$ and convert it to a mask probability:
\begin{equation}
    p_{mask}(t) = p_{min} + (p_{max} - p_{min})\frac{t}{T}.
\end{equation}
Only DNA base positions are maskable; condition tokens and special tokens are never used as prediction targets.
The model receives the corrupted sequence $\tilde{x}$ and predicts the original base at masked positions:
\begin{equation}
    \mathcal{L}(\theta) = - \sum_{i \in M} \log p_\theta(x_i \mid \tilde{x}, c),
\end{equation}
where $M$ is the set of masked positions.

This formulation makes the mask ratio an explicit control knob.
Biologically, it can be interpreted as a mutation budget.
Small $p_{mask}$ values produce conservative local edits, analogous to sparse mutation events.
Large $p_{mask}$ values explore larger sequence changes.
The fully masked case corresponds to generating an enhancer without relying on a reference sequence.
This differs from autoregressive generation, which produces a sequence through a fixed left-to-right order and does not expose a direct control over how much of the original sequence is preserved.

\subsection{Sampling}

For de novo diffusion sampling, the model starts from a condition token followed by $L$ mask tokens.
At each reverse step, the model predicts base distributions for currently masked positions.
A subset of masked positions is selected and filled with bases sampled from the restricted vocabulary $\{A,C,G,T\}$.
For mutation-like sampling, a reference sequence is first corrupted according to a chosen mask ratio $\rho$ and the model regenerates only the masked positions.

The current implementation evaluates the de novo setting with $L=246$ and $T=64$.
\todoresult{Insert mutation-ratio experiments: e.g., $\rho \in \{0.05,0.10,0.25,0.50,1.00\}$ once implemented.}

\subsection{Evaluation Metrics}

We evaluate generated sequences along four axes.

\paragraph{Functional activity.}
We use the activity predictor to compute $\hat{y}_0$, $\hat{y}_1$, and $\hat{y}_0+\hat{y}_1$.
For conditioned generation, we measure whether predicted activity follows the target bucket order high $>$ mid $>$ low.
We also report target-hit rate and positive-delta rate against matched reference sequences.

\paragraph{Sequence quality and diversity.}
We report valid DNA rate, unique rate, sequence length, maximum homopolymer length, pairwise Hamming distance, and nearest-reference Hamming distance.

\paragraph{Distributional fidelity.}
We compare generated and reference sequences by GC content and $k$-mer Jensen--Shannon divergence.
For diffusion models, we additionally report pseudo-log-likelihood:
\begin{equation}
    PLL(x) = \frac{1}{|B|}\sum_{i \in B}\log p_\theta(x_i \mid x_{\setminus i}, c),
\end{equation}
where $B$ is the set of DNA base positions.

\paragraph{Regulatory grammar.}
When motif annotations are available, we scan generated and reference sequences against a motif database and compare motif enrichment, hit rates, and positional distributions.
\todoresult{Fill motif database and threshold, or mark motif analysis as optional if no JASPAR file is used.}

\section{Experiments}

\subsection{Dataset and Implementation Details}

We use the DeepSTARR enhancer activity dataset with train, validation, and test splits.
\todoresult{Insert dataset split statistics: number of sequences, sequence length distribution, label mean/std.}
Sequences are bucketed using the training split only, and the same thresholds are applied to validation and test data.

The autoregressive baselines are fine-tuned from a GENERator eukaryotic genomic foundation model.
The masked diffusion generator is fine-tuned from a GENERanno masked language model.
\todoresult{Insert exact model checkpoints, GPU type, batch size, epochs, learning rate, and training time.}

\begin{table}
\caption{Dataset statistics. Values will be filled after running the data summary script.}
\label{tab:dataset}
\centering
\begin{tabular}{lrrrr}
\toprule
Split & Sequences & Median length & Mean label 0 & Mean label 1 \\
\midrule
Train & \todoresult{N} & \todoresult{L} & \todoresult{mean0} & \todoresult{mean1} \\
Valid & \todoresult{N} & \todoresult{L} & \todoresult{mean0} & \todoresult{mean1} \\
Test & \todoresult{N} & \todoresult{L} & \todoresult{mean0} & \todoresult{mean1} \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Predictor Reliability}

The activity predictor is the functional oracle for evaluating generated enhancers.
Therefore, its held-out performance must be established before interpreting generation results.
On the DeepSTARR test split, the predictor reaches an overall Pearson correlation of 0.652 and $R^2$ of 0.417.
Performance differs across the two activity dimensions: label 1 is predicted more accurately than label 0, with Pearson correlations 0.727 and 0.581, respectively.
This predictor is sufficiently informative for relative in silico comparison, but its moderate error motivates reporting sequence-distribution metrics alongside predictor activity.

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/predictor_metrics.png}
\caption{Predictor validation on the DeepSTARR test split. The final figure should include true-vs-predicted scatter plots for both activity dimensions and a summary of Pearson, $R^2$, and MAE.}
\label{fig:predictor}
\end{figure}

\begin{table}
\caption{Activity predictor performance.}
\label{tab:predictor}
\centering
\begin{tabular}{lrrr}
\toprule
Metric & Label 0 & Label 1 & Overall \\
\midrule
Pearson & 0.581 & 0.727 & 0.652 \\
$R^2$ & 0.337 & 0.494 & 0.417 \\
MAE & 0.627 & 0.554 & 0.590 \\
MSE & 0.671 & 0.539 & 0.605 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Autoregressive Generation Baselines}

We first compare unconditional and bucket-conditioned autoregressive generation.
The unconditional model tests whether the foundation model can generate valid enhancer-like continuations.
The conditioned model tests whether a simple activity token can bias generation toward desired activity ranges.

The unconditional AR baseline has valid DNA rate 1.000, unique rate 0.479 in its generation summary, and mean base-prediction accuracy 0.300 for continuation against matched references.
The conditioned AR baseline similarly has valid DNA rate 1.000, unique rate 0.466, and mean base-prediction accuracy 0.297.
After predictor scoring and sequence deduplication in the unified metrics table, both AR outputs have unique generated sequences but retain the same low-complexity composition issue.
Autoregressive generation achieves perfect DNA validity in our validation runs, but the generated continuations show a strong compositional artifact.
The unconditional AR model has mean GC content 0.255 and mean maximum homopolymer length 81.35, compared with 0.417 and 5.77 for reference sequences.
The conditioned AR model exhibits the same pattern, with mean GC content 0.255 and mean maximum homopolymer length 79.05.
Although these AR samples obtain relatively high predictor scores, the sequence-level artifacts suggest that the predictor can be exploited by repetitive low-complexity continuations.
This motivates a diffusion formulation that better preserves the natural sequence distribution.

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/fig_generator_quality_summary.png}
\caption{Autoregressive generation quality. The final figure should compare valid DNA rate, unique rate, bp accuracy, GC content, and homopolymer length.}
\label{fig:ar-quality}
\end{figure}

\subsection{Controllability of Bucket-Conditioned Generation}

For controllable enhancer design, generated sequences should not merely have high average predicted activity; they should match the requested bucket.
We therefore compare predictor score distributions for low, middle, and high conditions.
For diffusion, the generated high-activity bucket has the highest mean predictor score among generated buckets ($-3.627$), while low and mid buckets are lower ($-3.998$ and $-4.000$).
However, the separation is weaker than the reference bucket separation, where the high bucket reaches $-2.909$.
For conditioned AR generation, bucket-level control is not reliable: the low bucket has a higher mean predictor score ($-3.699$) than the mid bucket ($-3.794$), and the high bucket only modestly improves to $-2.911$.
Thus, the present conditioning mechanism provides partial activity bias but does not yet solve precise target-bucket control.

A key diagnostic is the two-dimensional activity space.
If bucket construction uses $y_0+y_1$, a model may improve one activity dimension while degrading the other.
Such behavior would inflate scalar activity while failing to preserve the full biological objective.
Across both AR baselines, the apparent scalar activity improvement is driven primarily by label 0.
For example, conditioned AR improves label 0 by $+0.479$ relative to matched references but decreases label 1 by $-0.188$ on average.
This confirms that scalar bucket construction from $y_0+y_1$ can hide trade-offs between the two DeepSTARR output dimensions.

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/fig_predicted_activity_by_method.png}
\caption{Controllability analysis. The final figure should include predicted activity by bucket, delta relative to matched references, and a two-dimensional label 0 vs label 1 scatter plot.}
\label{fig:controllability}
\end{figure}

\subsection{Mask-Ratio Controlled Diffusion}

The distinctive feature of \methodname{} is the ability to choose the mask ratio.
This enables a continuum from mutation-like local editing to fully de novo generation.
We evaluate at least two settings:
\begin{itemize}
    \item \textbf{De novo generation}: $\rho=1.0$, all bases are initially masked.
    \item \textbf{Mutation-like generation}: $\rho<1.0$, only a selected fraction of bases is masked and regenerated.
\end{itemize}

The current completed run evaluates the de novo diffusion setting and one preliminary low-mask ablation.
The full mask-ratio sweep is still required before making a strong claim about mutation-budget control.
We expect small mask ratios to preserve sequence identity and regulatory grammar while allowing modest activity shifts.
Larger mask ratios should increase diversity and activity exploration but may move farther from the reference distribution.

\begin{figure}
\centering
\fbox{\parbox{0.92\textwidth}{\centering TODO-FIGURE: full mask-ratio sweep. One low-mask ablation is available, but the 0.30--0.90 settings should be completed before finalizing this figure.}}
\caption{Mask-ratio tradeoff. Low mask ratios correspond to local mutations, while high mask ratios approach de novo generation. The final figure should plot predicted activity, nearest-reference distance, k-mer divergence, and motif preservation across mask ratios.}
\label{fig:mask-ratio}
\end{figure}

\subsection{Autoregressive vs Diffusion Comparison}

We compare all methods under a unified evaluation protocol.
The central hypothesis is that diffusion should provide better control over how much sequence is changed, while autoregressive generation may achieve valid DNA generation but has weaker control over mutation magnitude.

\begin{table}
\caption{Generator comparison on the validation split. Predictor score is $\hat{y}_0+\hat{y}_1$ when available. Lower $k$-mer JS divergence indicates closer reference distribution.}
\label{tab:generator-comparison}
\centering
\begin{tabular}{lrrrrrr}
\toprule
Method & Valid & Unique & Activity & Homopolymer & 4-mer JS & NN dist \\
\midrule
GC-matched random & 1.000 & 1.000 & -- & 4.92 & 0.0140 & 157.92 \\
AR unconditional & 1.000 & 1.000 & -3.582 & 81.35 & 0.1593 & 131.14 \\
AR conditioned & 1.000 & 1.000 & -3.546 & 79.05 & 0.1600 & 131.49 \\
Diffusion conditioned & 1.000 & 1.000 & -3.845 & 5.66 & 0.0006 & 148.05 \\
Reference & 1.000 & 1.000 & -- & 5.77 & 0.0000 & 117.77 \\
\bottomrule
\end{tabular}
\end{table}

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/fig_generation_gc_content.png}
\caption{Unified comparison of autoregressive and diffusion generation. The final figure should visualize activity, diversity, distributional fidelity, and diffusion PLL.}
\label{fig:tradeoff}
\end{figure}

\subsection{Regulatory Grammar Analysis}

Finally, we compare regulatory motif composition between generated and reference sequences.
This analysis tests whether generated enhancers preserve motif-level grammar rather than merely optimizing a predictor.
Motif analysis has not yet been completed because no motif database file was included in the downloaded results.
We therefore treat motif grammar as future validation in the present draft.

\begin{figure}
\centering
% \includegraphics[width=\textwidth]{figures/fig_motif_grammar.pdf}
\fbox{\parbox{0.92\textwidth}{\centering TODO-FIGURE: motif enrichment and motif hit-rate heatmap.}}
\caption{Regulatory motif grammar. The final figure should compare motif hit rates and positional distributions across reference, AR-generated, and diffusion-generated sequences.}
\label{fig:motifs}
\end{figure}

\section{Discussion}

Our central argument is that enhancer generation should be viewed as controlled exploration of regulatory sequence space.
Autoregressive generation is a natural baseline, but it imposes a left-to-right synthesis process.
Masked diffusion offers a different inductive bias: it can preserve most of a sequence while mutating only a selected subset of bases.
This is closer to an evolutionary view of sequence design, where variation is introduced through mutation and selection rather than complete rewriting.

The mask ratio is therefore more than a technical hyperparameter.
It provides an interpretable control over mutation magnitude.
A small mask ratio can be used for conservative enhancer optimization, where the objective is to improve activity while preserving known regulatory grammar.
A large mask ratio can be used for de novo discovery, where the goal is to explore novel sequence regions.
This makes mask-ratio controlled diffusion attractive for biological design settings where both innovation and preservation matter.

Several limitations remain.
First, predictor-guided evaluation can overestimate biological activity if generated sequences exploit predictor artifacts.
Second, activity bucket labels based on $y_0+y_1$ may hide conflicts between the two DeepSTARR activity dimensions.
Third, motif analysis is only a proxy for regulatory grammar and does not replace experimental validation.
Future work should incorporate predictor-based reward optimization, motif-aware constraints, and wet-lab validation of selected candidates.

\section{Conclusion}

We introduced a mask-ratio controlled diffusion perspective for enhancer sequence generation.
By interpreting the mask ratio as a mutation budget, the method unifies local enhancer editing and de novo generation within a single framework.
The proposed evaluation protocol compares autoregressive and diffusion generators across functional activity, diversity, distributional fidelity, and motif grammar.
Our current validation results show that diffusion improves distributional naturalness over AR baselines, while AR baselines obtain higher predictor scores at the cost of severe sequence artifacts.
This supports the use of masked diffusion as a more conservative and biologically plausible generator, but additional mask-ratio, test-split, seed, and motif analyses are needed before claiming robust activity optimization.

\begin{credits}
\subsubsection{\ackname}
\todoresult{Fill funding or acknowledgment information.}

\subsubsection{\discintname}
The authors have no competing interests to declare that are relevant to the content of this article.
\end{credits}

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