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DiMOS: Doob-Guided Inference-Time Multi-Objective Search for Scientific Design

Ziqing Wang, Qijie Zhu, Weimin Wu, Zeqi Ye, Minshuo Chen, Han Liu, Kaize Ding

arXiv:2610.05808v1cs.AI

TL;DR

Scientific sequence design requires jointly satisfying multiple objectives and constraints, but frozen-model guidance must handle non-differentiable rewards and search limited feasible regions efficiently. DIMOS uses reward-only approximate Doob-guided local resampling and budget-efficient trajectory search. Across DNA, protein, and RNA tasks, it achieves the highest joint success at matched generation times, up to 1.98× the strongest baseline on DNA and protein.

  • Problem

    Frozen masked diffusion models do not ensure objective satisfaction by sampling alone, while non-differentiable rewards and small feasible regions challenge efficient inference-time guidance.

    Source: §1 · pp. 1–2, §4.3 · p. 7

  • Method

    DIMOS combines reward-only approximate Doob-guided local resampling with budget-efficient trajectory search over promising continuations.

    Source: §1 · p. 2

  • Results

    DIMOS attains the highest joint success rate across six DNA, protein, and RNA tasks at matched wall-clock budgets, up to 1.98× the strongest baseline on DNA and protein.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Across the evaluated tasks, DIMOS improves joint success while retaining diverse designs.

    Source: §6 · p. 10

    The stated Doob-transform result assumes the guided sampler starts from the same fixed initial state as the original sampler.

    Source: §3.2 · p. 4

Abstract

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Scientific design often requires jointly satisfying multiple objectives and constraints. Pretrained masked diffusion models provide a generative foundation for this task, but fine-tuning them to meet these objectives and constraints incurs additional training costs, motivating inference-time guidance with frozen models. However, such guidance faces two challenges: pass-or-fail constraints and black-box reward models may provide no useful gradients, while jointly satisfying multiple requirements can leave a small feasible region, making feasible designs difficult to find within a limited inference budget. To address these challenges, we introduce DiMOS, a training-free framework for multi-objective scientific design. Using joint rewards from candidate completions, DiMOS performs approximate Doob-guided local resampling without requiring reward gradients. To allocate computation efficiently, it uses budget-efficient trajectory search to focus computation on promising continuations. Across six DNA, protein, and RNA tasks, DiMOS attains the highest joint success rate at comparable generation times, up to $1.98\times$ the strongest baseline on DNA and protein, while maintaining high sequence uniqueness and naturalness.

1 INTRODUCTION

Multi-objective sequence design seeks candidates that meet several objectives and constraints, but frozen-model guidance must handle non-differentiable rewards and find feasible designs efficiently. DIMOS combines reward-based local resampling with budget-efficient trajectory search and achieves the highest joint success across six tasks at matched generation times.

1 INTRODUCTION

  • Scientific sequence design seeks candidates that jointly meet multiple objectives and constraints, such as cell-specific activity or translation and stability.The examples include regulatory DNA with target-cell activity and limited off-target activity, and therapeutic mRNA with efficient translation and sufficient stability.Source: §1 · p. 1
  • Frozen masked diffusion models provide a generative prior, but sampling alone does not ensure objectives are met, while fine-tuning adds costs when objectives or thresholds change.Inference-time guidance reuses the frozen prior and scores candidates with a joint reward that is high only when every requirement is met.Source: §1 · p. 1
  • Pass-or-fail constraints and black-box reward models may provide no useful gradients, while a small feasible region can make jointly successful designs costly to find within a limited budget.The passage cites ViennaRNA as a black-box RNA-folding tool and notes that gradient-based inference-time methods struggle to follow such rewards.Source: §1 · pp. 1–2
  • DIMOS uses reward evaluations alone for approximate Doob-guided local resampling, then allocates computation toward promising continuations with budget-efficient trajectory search.The framework keeps masked diffusion models frozen and supports black-box objectives and hard constraints.Source: §1 · p. 2
  • Up to 1.98× the strongest baseline on DNA and protein; DIMOS attains the highest joint success rate across six tasks under matched wall-clock budgets while maintaining sequence naturalness.The tasks span DNA, protein, and RNA design.Source: §1 · p. 2

2 RELATED WORK

Prior work addresses multi-objective design and training-free adaptation through several search and guidance strategies. DIMOS focuses on finding sequences that jointly satisfy specified thresholds using inference-time search with reward evaluations.

2 RELATED WORK

  • Pareto optimality does not ensure simultaneous satisfaction of application thresholds, so this work focuses on inference-time search for designs that jointly meet specified property thresholds.Prior approaches include discrete diffusion, constrained reinforcement learning, multi-objective Bayesian optimization, peptide tree search, and rank-directional flow guidance.Source: §2 · p. 2
  • Training-free adaptation steers a frozen prior at sampling time through gradient guidance, particle methods, or evaluation-based guidance, with iterative refinement as an orthogonal outer loop.The cited approaches include gradient-based approximations [Nisonoff et al., 2025; Schiff et al., 2025], particle methods [Wu et al., 2023; Singhal et al., 2025], and evaluation-based guidance [Guo et al., 2024; Li et al., 2025].Source: §2 · pp. 2–3
  • DIMOS uses reward evaluations alone for approximate Doob-guided local resampling, then concentrates computation on promising continuations through shared prefixes and branch selection.Related probabilistic formulations connect adaptation to Doob’s h-transform, soft value functions, and posterior sampling.Source: §2 · p. 3

3 PRELIMINARIES

The preliminaries introduce discrete diffusion for sequence generation and Doob’s h-transform for terminal-reweighted guidance. They define the masked diffusion setting and explain how reward preferences can be propagated backward to alter reverse transitions.

3.1 DISCRETE DIFFUSION

  • Discrete diffusion defines a forward corruption process and a reverse process that progressively removes corruption to recover the data distribution.The forward process is chosen so its terminal distribution approaches a tractable reference distribution; reverse dynamics depend on density ratios between states.Source: §3.1 · p. 3
  • Masked discrete diffusion independently replaces clean tokens with a mask symbol, and as the masking probability approaches one the terminal distribution approaches the fully masked reference.The process progressively masks tokens and never directly changes one clean token into another.Source: §3.1 · p. 3
  • The reverse dynamics are parameterized by the clean-token posterior, approximated with μ^j_{θ,t}, and the reverse process is simulated on a finite denoising grid from t0 = 0 to tL = T.At inference, η = 1 recovers the denoiser distribution; η < 1 sharpens it, and η > 1 flattens it.Source: §3.1 · pp. 3–4

3.2 DIFFUSION GUIDANCE VIA DOOB’S h-TRANSFORM

  • Reward tilting defines a terminal distribution from the pretrained model and a reward; soft objectives and hard constraints can share this formulation.For a hard constraint, the indicator-based reward approaches exact conditioning on the feasible set as the penalty P tends to infinity.Source: §3.2 · p. 4
  • Doob’s h-function propagates terminal preference backward through the original reverse process, acting as a soft value function for the corresponding control problem.The h-function is defined as a conditional expectation of the terminal weight given the current state.Source: §3.2 · p. 4
  • Reweighting reverse transitions with the h-function yields a valid Markov kernel and the desired terminal marginal when the guided sampler starts from the same fixed initial state.For masked discrete diffusion, the sampler starts from the fully masked state, satisfying this fixed-initial-state condition.Source: §3.2 · pp. 4–5

4 METHOD

DiMOS guides a frozen masked diffusion model with joint-reward evaluations, then allocates inference computation toward promising continuations. Its method combines requirement-specific gating, approximate Doob-guided local resampling, and budget-efficient trajectory search.

4 METHOD

  • DiMOS combines joint-reward feedback, approximate Doob-guided local resampling, and budget-efficient trajectory search for multi-objective design with a frozen masked diffusion model.The method compares candidate updates without reward gradients and focuses computation on promising continuations.Source: §4 · p. 5

4.1 JOINT REWARD FOR MULTIPLE REQUIREMENTS

  • Per-property hard or soft gates are aggregated in log space, preserving feedback about individual requirements while using the same feasibility criteria.The method uses per-property thresholds rather than directly maximizing a weighted sum, which does not generally guarantee joint feasibility.Source: §4.1 · p. 5

4.2 APPROXIMATE DOOB-GUIDED LOCAL RESAMPLING

  • At each guided step, DiMOS enumerates likely tokens at the highest-entropy newly revealed position and samples an update using completion-based candidate values.Each update uses at most M reward evaluations and requires no reward gradients.Source: §4.2 · p. 6
  • When M = |V|, the truncation term vanishes; with accurate completion-based values, discrepancy is primarily controlled by variation in the shared-context value.The theorem's error analysis separates top-M truncation, context-reweighting, and value-estimation errors.Source: §4.2 · pp. 6–7

4.3 BUDGET-EFFICIENT TRAJECTORY SEARCH

  • Trajectory search shares denoising prefixes across branches, then uses estimated joint rewards to refine branches and return each group's highest-reward final design.Group-local selection helps preserve sequence uniqueness, while prefix sharing reduces state updates from KL to s + K(L − s) per group.Source: §4.3 · p. 7

5 EXPERIMENTS

Experiments evaluate DIMOS on DNA, protein, and RNA design, emphasizing joint success and design quality under hard- and soft-gate conditions. Results show strong joint success at comparable budgets, with task-specific search allocation.

5.2 MAIN RESULTS

  • DIMOS leads DNA and protein across both gate modes in joint SR, nearly doubling SVDD in soft-gate mode while retaining high uniqueness and quality.It retains 100% uniqueness on DNA and over 99.9% on protein under both gate modes, as well as over 92% protein fold recovery.Source: Table 2 · p. 8, §5.2 · p. 8

5.1 EXPERIMENTAL SETUP

  • Experiments test DNA Activity + ATAC and protein ∆∆G + SeqRec under hard/soft gates, against sampling, gradient-based, and gradient-free baselines.Joint SR, objective medians, uniqueness, naturalness, validity, and generation time are evaluated; results report mean ± s.d. over three seeds.Source: §5 · p. 7, §5.1 · p. 8

5.3 HYPERPARAMETER ANALYSIS AND ABLATION

  • Increasing M and K generally improves joint SR with diminishing gains, while delayed branching favors DNA and earlier branching favors protein.DNA maintains high success when branching is delayed through roughly the first half of denoising; the allocation should reflect the task.Source: Figure 3 · p. 9, §5.3 · p. 9
  • Doob-guided local feedback causes the largest ablation loss; distinct candidate enumeration matters more for protein, while multiple branches and intermediate refinement matter especially for DNA.Adding the search layer to the SVDD kernel improves it but closes under a fifth of the gap to DIMOS.Source: Table 3 · p. 9, §5.3 · p. 9

5.4 EFFICIENCY UNDER TIME BUDGETS

  • At baseline-matched time budgets, DIMOS attains higher joint SR; matching or exceeding SVDD requires approximately 63% less DNA and 74% less protein generation time.The Figure 4 budget envelopes show the empirical joint-success versus generation-time trade-off for DNA and protein.Source: Figure 4 · p. 9, §5.4 · pp. 9–10

6 CONCLUSION

The conclusion presents DIMOS as a training-free approach to multi-objective sequence design with frozen masked diffusion models. Across DNA, protein, and RNA experiments, it reports improved joint success while retaining diverse designs and identifies task-dependent search-allocation trade-offs.

6 CONCLUSION

  • DIMOS combines approximate Doob-guided local resampling and budget-efficient trajectory search to improve joint success across DNA, protein, and RNA while retaining diverse designs.Its allocation studies highlight task-dependent trade-offs among candidate width, branching, and search duration.Source: §6 · p. 10

A PROOF OF PROPOSITION 1

The proof connects the Doob-transformed reverse process to its terminal-reweighted distribution, then analyzes the practical coordinate-wise kernel and its approximation errors. Branch-level pruning is outside the sampling bound because it serves search rather than exact sampling.

A PROOF OF PROPOSITION 1

  • The transformed path law has terminal distribution proportional to the original terminal distribution times the positive terminal weight.The proof substitutes the h-function definition into the path-law expression to obtain the terminal-reweighted distribution.Source: A PROOF OF PROPOSITION 1 · p. 14

B PROOF OF THEOREM 1

  • The practical successor state is represented by a context and selected token, yielding a kernel that factors into context and token conditionals.The practical resampling rule leaves the context sampling unchanged and uses a completion-based value approximation for token selection.Source: B PROOF OF THEOREM 1 · p. 15
  • The kernel discrepancy is bounded by separating context-reweighting, top-M truncation, and value-estimation errors.The proof applies the triangle inequality to combine the component bounds.Source: B PROOF OF THEOREM 1 · pp. 15–16
  • Branch-level pruning serves search and lies outside the bound for exact sampling from the terminal-reweighted distribution.The bound concerns the practical kernel approximation, not the subsequent branch-selection step.Source: B PROOF OF THEOREM 1 · p. 16

C EMPIRICAL EVALUATION OF LOCAL APPROXIMATION ERROR

The local resampling kernel closely matches the exact Doob transition in a near-terminal evaluation. The section also explains finite hard-gate penalties and specifies the search schedule, completion rules, and success criteria.

C EMPIRICAL EVALUATION OF LOCAL APPROXIMATION ERROR

  • Median TV is below 0.001 for DNA and protein under both gate modes and below 0.023 for RNA with three MASK positions remaining.These measurements compare the practical kernel with the reference Doob transition on 24 partially generated sequences per domain.Source: C EMPIRICAL EVALUATION OF LOCAL… · p. 17, Table 4 · p. 17

D WHY THE HARD-GATE PENALTY IS FINITE

  • A finite hard-gate penalty keeps local resampling normalizable when all candidates violate a requirement, while a common violation penalty cancels during normalization.Hard gates distinguish candidates across the threshold but do not rank candidates on the same side; soft gates also distinguish margins.Source: D WHY THE HARD-GATE PENALTY IS FINITE · p. 17

E ALGORITHM AND IMPLEMENTATION DETAILS

E.1 SAMPLING SCHEDULE AND TRANSITION NOTATION

  • Branching occurs at split step s, while token enumeration begins with the first guided update independently of the split step.The denoising schedule defines branch-selection checkpoints between the split and final update.Source: §E.1 · p. 18

E.3 COMPLETION AND BRANCH REWARD ESTIMATION

  • Completion preserves committed tokens and fills remaining masks stochastically for DNA and by argmax for protein and RNA.DNA completions share random numbers across a parent’s candidates.Source: §E.3 · p. 18

F EVALUATION CRITERIA

  • The evaluation criteria cover task-specific success thresholds and metrics for joint feasibility, design quality, diversity, validity, and efficiency.The final criteria are shared across methods and gate modes within each task.Source: F EVALUATION CRITERIA · p. 18, §F.1 · p. 18

F.1 TASK SUCCESS THRESHOLDS

  • Both objective conditions must be satisfied for a design to meet the canonical joint-success criteria.The task-specific criteria are listed in Table 6.Source: Table 6 · p. 19

F.2 METRIC DEFINITIONS

The section defines how the study measures joint success, objective quality, diversity, validity, and generation efficiency.

F.2 METRIC DEFINITIONS

  • Joint success rate is the fraction of returned designs satisfying both canonical objective thresholds.For RNA, evaluation uses held-out Optimus-MRL with the structural criterion, while generation is guided by ConvGRU-MRL.Source: §F.2 · p. 19
  • Objective quality reports each objective’s median across all outputs and among the ten designs ranked highest by joint reward.The top ten are ranked by joint reward rather than by either objective alone.Source: §F.2 · p. 19
  • Diversity and validity include exact-sequence uniqueness, DNA naturalness, and protein fold recovery.DNA naturalness uses 3-mer and JASPAR motif-profile correlations; protein fold recovery reports fractions with scRMSD < 2Å and pLDDT > 80.Source: §F.2 · pp. 19–20
  • Efficiency is generation time per returned design, reported in milliseconds and not used to rank methods.Timings within each table come from one measurement batch, with one process per GPU and kernel compilation disabled.Source: §F.2 · p. 20
  • Main-table entries are reported as mean ± population standard deviation over three independent seeds.Source: §F.2 · p. 20

G BASELINE AND BUDGET PROTOCOL

The protocol fixes task generators and reward settings, compares DIMOS with several sampling and guidance baselines, and calibrates selected candidate-count baselines to DIMOS’s generation budget.

G BASELINE AND BUDGET PROTOCOL

  • DNA designs use the pretrained DRAKES generator in the 200-bp GOSAI setting, while protein generation uses DRAKES with 12 held-out backbones.Source: G BASELINE AND BUDGET PROTOCOL · p. 20
  • The baselines include pretrained sampling, budget-calibrated BEST-OF-N, TDS, SMC, FK-STEERING, and SVDD-PM.RNA excludes TDS because neither selected task supplies a differentiable full joint reward.Source: G BASELINE AND BUDGET PROTOCOL · p. 20
  • DIMOS and reward-based baselines share reward parameters within each task and gate mode, with hard-gate mode applying a binary gate to one requirement.The hard-gated requirement is Activity for DNA, ∆∆G for protein, or MRL for RNA; the other requirement retains its soft gate.Source: G BASELINE AND BUDGET PROTOCOL · p. 20, Table 7 · p. 20
  • BEST-OF-N and SVDD candidate counts are set to the closest measured generation budget to DIMOS that is not cheaper.Source: G BASELINE AND BUDGET PROTOCOL · p. 20
  • Methods return the same number of designs within each domain, and task definitions, frozen priors, and evaluation reward models are fixed across methods.DNA activity and protein ddG use evaluation checkpoints separate from those used for guidance; generation wall time is normalized by returned designs.Source: G BASELINE AND BUDGET PROTOCOL · p. 20

H SEPARATING THE SEARCH LAYER FROM THE LOCAL KERNEL

The search layer improves SVDD-PM’s joint success under matched budgets, but the local kernel accounts for the larger share of DIMOS’s advantage. Additional tests cover DNA specificity and protein hydrophilicity, including a protein task where TDS never satisfies the hydrophilicity requirement.

H SEPARATING THE SEARCH LAYER FROM THE LOCAL KERNEL

I.1 DNA CELL-TYPE SPECIFICITY

  • Activity and specificity are in tension because higher HepG2 activity tends to accompany higher off-target activity; under a hard activity gate, pass rates fall and designs drift toward uniform composition.The task pairs HepG2 activity with a specificity margin against K562 and SK-N-SH; MaxGap retains a soft gate.Source: §I.1 · p. 22, Table 10 · p. 22

I.2 PROTEIN HYDROPHILICITY (GRAVY)

  • TDS has 0.00% joint success in both protein hydrophilicity gate modes, despite clearing the binding threshold on approximately 52–54% of designs.No TDS output satisfies the GRAVY < −0.70 requirement.Source: §I.2 · p. 22
  • At the budget-matched comparison, DIMOS reaches 27.39% joint success against 18.73% and 19.12%, at about 80 ms per design.The comparison uses Best-of-N at K=8 and SVDD at M=4; DIMOS also exceeds the strongest measured baseline at any budget.Source: §I.2 · p. 22

I.3 RNA DESIGN

The RNA experiments pair translation with accessibility or folding stability and show that the preferred translation gate depends on the remaining requirement. The section also evaluates continuous-score rewards for DNA and protein without retuning the configurations.

I.3 RNA DESIGN

  • 84.11% joint success under a hard translation gate exceeds 78.39% under a soft gate for RNA translation plus accessibility, while held-out translation pass rates remain 99.74% and 98.96%.Exact accessibility pass rates are 85.16% and 78.65%, respectively; hard-gate reward-guided baselines pass the opening proxy on 14–77% of designs but the exact criterion on only 1.6–4.7%.Source: §I.3 · p. 23, Table 12 · p. 23
  • 54.17% joint success and 62.50% held-out translation success under soft-gate guidance exceed 36.72% and 51.30% under hard-gate guidance for translation plus folding stability.The comparison uses 50-nt minimum free energy; translation is evaluated with held-out Optimus-5′, while folding energy uses the same ViennaRNA call for guidance and grading.Source: §I.3 · pp. 23–24, Table 13 · p. 24

J CONTINUOUS-SCORE REWARDS

  • The DNA and protein continuous-score tests replace threshold-gated rewards with weighted sums of standardized property scores, while keeping tasks, configurations, and success criteria unchanged and applying no retuning.The supplied passages describe the evaluation setup but do not report its results.Source: J CONTINUOUS-SCORE REWARDS · p. 24, Table 14 · p. 25, Table 15 · p. 26
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