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

cs.AIOct 5, 2026

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

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

Organizations: Northwestern University

Abstract

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.

Figures & tables

Figure 1: Joint success and uniqueness. Bubble area encodes within-task normalized 3-mer correlation (DNA), scRMSD

<2\,\text{\AA}

rate (protein), and Optimus-MRL (RNA). Three-seed means.

Figure 2: Overview of DiMOS . Top: multi-objective design with a frozen prior. Middle: $K$ branches from step $s$ , with reward-guided refinement. Bottom: $M$ token candidates are enumerated, completed, and stochastically resampled using prior and reward weights.

Method	Joint SR (%) $\uparrow$	Activity $\uparrow$		ATAC $\uparrow$		Uniq. (%)	3-mer $r$	JASPAR $r$	Time (ms)
		Median	Top-10	Median	Top-10				Time (ms)
Hard-Gate Mode
Pretrained	0.00 $\pm$ 0.00	0.18 $\pm$ 0.01	2.41 $\pm$ 0.39	0.03 $\pm$ 0.00	0.65 $\pm$ 0.06	100.00 $\pm$ 0.00	-0.04 $\pm$ 0.01	0.29 $\pm$ 0.01	8.46 $\pm$ 0.23
Best-of-N	2.34 $\pm$ 0.34	1.37 $\pm$ 0.12	5.32 $\pm$ 0.19	0.45 $\pm$ 0.01	0.90 $\pm$ 0.04	100.00 $\pm$ 0.00	0.76 $\pm$ 0.00	0.90 $\pm$ 0.00	271.56 $\pm$ 0.68
TDS	78.80 $\pm$ 6.63	4.80 $\pm$ 0.13	6.19 $\pm$ 0.21	0.84 $\pm$ 0.02	0.97 $\pm$ 0.01	48.12 $\pm$ 1.29	0.92 $\pm$ 0.03	0.91 $\pm$ 0.01	171.39 $\pm$ 0.18
SMC	76.04 $\pm$ 8.17	4.74 $\pm$ 0.11	6.25 $\pm$ 0.24	0.83 $\pm$ 0.03	0.97 $\pm$ 0.01	48.02 $\pm$ 2.62	0.92 $\pm$ 0.04	0.91 $\pm$ 0.01	89.28 $\pm$ 0.10

Table 1: DNA design with hard and soft gates. Activity + ATAC results with held-out activity evaluation. Both modes use the same success criteria, differing only in whether activity receives a hard gate (binary penalty) or a soft gate (smooth reward).

Method	Joint SR (%) $\uparrow$	$\Delta\Delta G$ $\uparrow$		SeqRec $\uparrow$		Uniq. (%)	scRMSD (%)	pLDDT (%)	Time (ms)
		Median	Top-10	Median	Top-10				Time (ms)
Hard-Gate Mode
Pretrained	4.04 $\pm$ 0.30	-0.45 $\pm$ 0.00	0.45 $\pm$ 0.03	0.44 $\pm$ 0.00	0.48 $\pm$ 0.00	99.67 $\pm$ 0.05	93.55 $\pm$ 0.11	87.98 $\pm$ 0.11	17.42 $\pm$ 0.08
Best-of-N	16.06 $\pm$ 0.19	-0.02 $\pm$ 0.01	0.70 $\pm$ 0.05	0.49 $\pm$ 0.00	0.52 $\pm$ 0.00	99.18 $\pm$ 0.03	92.84 $\pm$ 0.09	86.65 $\pm$ 0.16	159.89 $\pm$ 0.05
TDS	13.59 $\pm$ 0.48	-0.12 $\pm$ 0.01	0.38 $\pm$ 0.06	0.47 $\pm$ 0.00	0.50 $\pm$ 0.00	16.75 $\pm$ 0.24	93.12 $\pm$ 1.00	87.96 $\pm$ 0.21	124.49 $\pm$ 0.38
SMC	4.10 $\pm$ 0.30	-0.10 $\pm$ 0.06	0.69 $\pm$ 0.07	0.44 $\pm$ 0.00	0.48 $\pm$ 0.00	22.09 $\pm$ 0.74	92.90 $\pm$ 0.83	89.37 $\pm$ 0.03	83.11 $\pm$ 0.08

Table 2: Protein design with hard and soft gates.

\Delta\Delta G

+ SeqRec results with identical success criteria. The

\Delta\Delta G

term uses a hard gate (binary penalty) or a soft gate (smooth reward).

Figure 3: Sensitivity to

M

K

, and

s/T

. One parameter varies at a time.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Domain	Gate	Samples	Median TV	Mean TV
DNA	Soft	24	0.00041	0.00286
DNA	Hard	24	0.00012	0.00968
Protein	Soft	24	0.00073	0.09231
Protein	Hard	24	0.00031	0.03408
RNA	Soft	24	0.02280	0.03571
RNA	Hard	24	0.00123	0.01503

Appendix

Table 4: Local approximation error across domains. Each row summarizes

24

partially generated sequences with three remaining MASK positions.

Domain	Task	$T$	$M$	$K$	$s$	$\beta$	$\eta$
DNA	ATAC	$128$	$4$	$4$	$64$	$0.25$	$3.0$
DNA	MaxGap	$128$	$4$	$8$	$64$	$0.25$	$3.0$
Protein	SeqRec	$49$	$4$	$2$	$0$	$0.02$	$1.0$
Protein	GRAVY	$49$	$2$	$2$	$0$	$0.02$	$1.0$
RNA	Accessibility	$49$	$4$	$2$	$18$	$0.04$	$0.05$
RNA	MFE	$49$	$4$	$2$	$18$	$0.04$	$1.0$

Appendix

Table 5: Sampler configuration of the reported DiMOS runs , one row per task.

T

is the number of executed denoising steps,

M

the candidate width,

K

the branch width,

s

the split step,

\beta

the tilt temperature of Eq. ( 8 ), and

\eta

the proposal temperature.

Task	Objective 1	Objective 2
Activity + ATAC	Activity $\geq 4.0$	ATAC $\geq 0.7$
Activity + MaxGap	Activity $\geq 4.0$	MaxGap $\geq 1.0$
ddG + SeqRec	ddG $\geq 0$	SeqRec $\geq 0.55$
ddG + GRAVY	ddG $\geq 0$	GRAVY $\leq-0.70$
MRL + Opening dG	Opening dG $\leq 0.25$ kcal/mol	Optimus-MRL $\geq 0.45$
MRL + MFE	MFE $\leq-16$ kcal/mol	Optimus-MRL $\geq 0.45$

Appendix

Table 6: Canonical joint-success criteria for the six design tasks. Both objective conditions must be satisfied.

Domain	Reward Pair	$\tau_{1}$	$\tau_{2}$
DNA	Activity + ATAC	$0.5$	$0.05$
	Activity + MaxGap	$0.5$	$0.5$
Protein	$\Delta\Delta G$ + SeqRec	$0.3$	$0.03$
	$\Delta\Delta G$ + GRAVY	$0.3$	$0.10$
RNA	MRL + Opening $\Delta G$	$0.05$	$0.25$
	MRL + MFE	$0.05$	$1.0$

Appendix

Table 7: Shared soft-gate widths. The widths follow the reward order shown.

Method	$M$	$K$	$s$	Joint SR (%) $\uparrow$	3-mer $r$	Oracle	Time (ms)
Soft-Gate Mode
SVDD-PM (Tab. 1 )	$12$	$1$	–	55.16 $\pm$ 1.55	$0.74$	$1.97$ M	$244.7$
$+$ search, matched budget	$4$	$4$	$64$	63.02 $\pm$ 2.20	$0.73$	$1.96$ M	$251.0$
$+$ search, released $M$	$20$	$4$	$64$	84.43 $\pm$ 0.96	$0.79$	$8.51$ M	$1101.8$
DiMOS (Tab. 1 )	$4$	$4$	$64$	98.39 $\pm$ 0.29	$0.88$	$1.94$ M	$234.6$
Hard-Gate Mode

Appendix

Table 8: Separating the search layer from the local kernel. DNA activity–ATAC,

N=640

, three seeds. Rows marked Tab. 1 are reproduced from the main results. Oracle counts reward-model forward passes per seed; time is generation wall clock per returned design.

$M$	Oracle	Time (ms)	Joint SR (%) $\uparrow$		3-mer $r$
$M$	Oracle	Time (ms)	Soft	Hard	Soft	Hard
$4$	$0.66$ M	$84$	26.30 $\pm$ 0.83	18.59 $\pm$ 1.38	$0.69$	$0.64$
$8$	$1.31$ M	$159$	46.25 $\pm$ 1.00	37.71 $\pm$ 1.36	$0.72$	$0.68$
$10$	$1.64$ M	$184$	51.51 $\pm$ 1.67	43.07 $\pm$ 0.70	$0.73$	$0.69$
$12$ (Tab. 1 )	$1.97$ M	$245$	55.16 $\pm$ 1.55	45.05 $\pm$ 0.97	$0.74$	$0.69$
$16$	$2.62$ M	$336$	60.21 $\pm$ 2.78	51.56 $\pm$ 1.67	$0.75$	$0.71$

Appendix

Table 9: SVDD-PM candidate width on DNA activity–ATAC.

T=128

N=640

, three seeds, no search layer. Oracle and time are shared by the two gate modes to within

0.2\%

Method	Joint SR (%) $\uparrow$	Activity $\uparrow$		MaxGap $\uparrow$		Uniq. (%)	3-mer $r$	JASPAR $r$	Time (ms)
		Median	Top-10	Median	Top-10				Time (ms)
Hard-Gate Mode
Pretrained	0.00 $\pm$ 0.00	0.18 $\pm$ 0.01	2.84 $\pm$ 0.25	-0.12 $\pm$ 0.00	0.39 $\pm$ 0.30	100.00 $\pm$ 0.00	-0.04 $\pm$ 0.01	0.29 $\pm$ 0.01	8.48 $\pm$ 0.20
Best-of-N	1.20 $\pm$ 0.27	1.16 $\pm$ 0.05	4.49 $\pm$ 0.24	0.44 $\pm$ 0.00	2.37 $\pm$ 0.65	100.00 $\pm$ 0.00	0.40 $\pm$ 0.01	0.74 $\pm$ 0.00	273.38 $\pm$ 0.32
TDS	7.71 $\pm$ 4.23	4.37 $\pm$ 0.10	5.23 $\pm$ 0.20	-0.37 $\pm$ 0.20	1.88 $\pm$ 0.45	46.30 $\pm$ 1.62	0.77 $\pm$ 0.06	0.85 $\pm$ 0.04	171.94 $\pm$ 0.70
SMC	5.89 $\pm$ 1.42	4.35 $\pm$ 0.10	4.79 $\pm$ 0.13	-0.44 $\pm$ 0.07	2.11 $\pm$ 0.49	47.34 $\pm$ 3.77	0.79 $\pm$ 0.03	0.89 $\pm$ 0.01	75.43 $\pm$ 0.19

Appendix

Table 10: DNA cell-type specificity: Activity

+

MaxGap . HepG2 activity paired with a specificity margin against K562 and SK-N-SH. Unlike Activity

+

ATAC the two objectives are in tension. The activity term uses a hard gate or a soft gate, while MaxGap retains its soft gate. With a hard gate, activity’s own pass rate falls and the designs drift toward uniform composition. Uniqueness, 3-mer

r

and JASPAR

r

are guardrails, not objectives, and are reported without ranking.

N=640

per seed, mean

\pm

s.d. over three seeds; time is ms per design.

Method	Joint SR (%) $\uparrow$	$\Delta\Delta G$ $\uparrow$		GRAVY $\downarrow$		Uniq. (%)	scRMSD (%)	pLDDT (%)	Time (ms)
		Median	Top-10	Median	Top-10				Time (ms)
Hard-Gate Mode
Pretrained	6.84 $\pm$ 0.21	-0.45 $\pm$ 0.00	0.28 $\pm$ 0.02	-0.57 $\pm$ 0.00	-0.77 $\pm$ 0.00	99.67 $\pm$ 0.05	93.55 $\pm$ 0.11	87.98 $\pm$ 0.11	16.90 $\pm$ 0.08
Best-of-N	18.73 $\pm$ 0.16	-0.28 $\pm$ 0.00	0.44 $\pm$ 0.02	-0.75 $\pm$ 0.00	-0.86 $\pm$ 0.00	98.31 $\pm$ 0.09	93.55 $\pm$ 0.05	87.96 $\pm$ 0.14	81.64 $\pm$ 0.09
TDS	0.00 $\pm$ 0.00	0.18 $\pm$ 0.03	0.36 $\pm$ 0.04	0.43 $\pm$ 0.01	0.24 $\pm$ 0.01	11.11 $\pm$ 0.27	88.76 $\pm$ 0.35	84.38 $\pm$ 0.00	121.42 $\pm$ 0.75
SMC	16.93 $\pm$ 1.24	-0.28 $\pm$ 0.01	0.40 $\pm$ 0.06	-0.51 $\pm$ 0.00	-0.75 $\pm$ 0.01	22.59 $\pm$ 0.77	94.92 $\pm$ 0.63	86.65 $\pm$ 0.37	80.37 $\pm$ 0.06

Appendix

Table 11: Protein binder design,

\Delta\Delta G>0

and GRAVY

<-0.70

. Same gate modes and protocol as Table 2 . Best-of-N and SVDD are shown at the budget closest to DiMOS ’s wall clock, which in the hard-gate block is below their published budgets because DiMOS runs at

79

ms per design there. Time is milliseconds per design.

Method	Joint SR (%) $\uparrow$	Opening $\Delta G$ $\downarrow$		ConvGRU-MRL $\uparrow$		Uniq. (%)	Optimus-MRL $\uparrow$	Time (ms)
		Median	Top-10	Median	Top-10			Time (ms)
Hard-Gate Mode
Pretrained	0.52 $\pm$ 0.45	4.07 $\pm$ 0.17	2.01 $\pm$ 0.40	0.34 $\pm$ 0.08	0.81 $\pm$ 0.03	100.00 $\pm$ 0.00	-0.11 $\pm$ 0.11	10.69 $\pm$ 0.08
Best-of-N	1.04 $\pm$ 1.19	2.04 $\pm$ 0.08	0.73 $\pm$ 0.03	0.89 $\pm$ 0.01	0.88 $\pm$ 0.00	100.00 $\pm$ 0.00	0.55 $\pm$ 0.02	186.22 $\pm$ 0.32
FK-Steering	1.82 $\pm$ 1.80	2.25 $\pm$ 0.16	0.77 $\pm$ 0.26	0.81 $\pm$ 0.01	0.89 $\pm$ 0.02	100.00 $\pm$ 0.00	0.36 $\pm$ 0.04	725.52 $\pm$ 9.83
SMC	2.86 $\pm$ 4.30	0.93 $\pm$ 0.13	0.51 $\pm$ 0.10	0.93 $\pm$ 0.06	1.01 $\pm$ 0.10	28.39 $\pm$ 1.19	0.62 $\pm$ 0.04	202.26 $\pm$ 8.12

Appendix

Table 12: RNA 5 ′ UTR design with hard and soft gates. Both blocks are the same translation

+

accessibility task with the same success criterion, and differ only in whether the translation term uses a hard gate (binary penalty) or a soft gate (smooth reward).

N{=}128

designs per seed. Both objectives are graded by held-out oracles : guidance sees a ConvGRU MRL predictor and a constrained-MFE opening proxy, while the table reports Optimus-5 ′ MRL and the exact partition-function opening energy

-RT\log p_{\mathrm{unpaired}}

, a different physical quantity rather than a finer estimate of the proxy. Each baseline is shown at its measured time-closest budget rung; none runs below our budget. Mean

\pm

s.d. over three seeds; time is milliseconds per design.

Method	Joint SR (%) $\uparrow$	MFE $\downarrow$		ConvGRU-MRL $\uparrow$		Uniq. (%)	Optimus-MRL $\uparrow$	Time (ms)
		Median	Top-10	Median	Top-10			Time (ms)
Hard-Gate Mode
Pretrained	0.26 $\pm$ 0.45	-8.57 $\pm$ 0.53	-12.13 $\pm$ 1.69	0.34 $\pm$ 0.08	0.75 $\pm$ 0.02	100.00 $\pm$ 0.00	-0.11 $\pm$ 0.11	10.73 $\pm$ 0.23
Best-of-N	0.78 $\pm$ 1.35	-9.38 $\pm$ 0.23	-12.72 $\pm$ 0.88	0.85 $\pm$ 0.01	0.84 $\pm$ 0.01	100.00 $\pm$ 0.00	0.47 $\pm$ 0.02	78.81 $\pm$ 2.70
FK-Steering	2.08 $\pm$ 0.45	-11.39 $\pm$ 0.18	-14.29 $\pm$ 1.16	0.72 $\pm$ 0.03	0.84 $\pm$ 0.01	100.00 $\pm$ 0.00	0.32 $\pm$ 0.06	140.91 $\pm$ 1.77
SMC	18.75 $\pm$ 7.53	-14.77 $\pm$ 0.89	-16.10 $\pm$ 0.62	0.85 $\pm$ 0.01	0.85 $\pm$ 0.02	21.09 $\pm$ 4.13	0.46 $\pm$ 0.02	68.72 $\pm$ 0.93

Appendix

Table 13: RNA 5 ′ UTR design, translation

+

folding stability. As in Table 12 , with accessibility replaced by the 50-nt minimum free energy. MRL is graded by the held-out Optimus-5 ′ predictor; MFE has no cheaper guidance proxy and is the one objective shared between guidance and grading. Mean

\pm

s.d. over three seeds; time is milliseconds per design.

Method	Joint SR (%) $\uparrow$	Activity $\uparrow$		ATAC $\uparrow$		Uniq. (%)	3-mer $r$	JASPAR $r$	Time (ms)
		Median	Top-10	Median	Top-10				Time (ms)
$\lambda=0.25$ : ATAC-leaning
Pretrained	0.00 $\pm$ 0.00	0.18 $\pm$ 0.01	2.41 $\pm$ 0.39	0.03 $\pm$ 0.00	0.65 $\pm$ 0.06	100.00 $\pm$ 0.00	-0.04 $\pm$ 0.01	0.29 $\pm$ 0.01	8.13 $\pm$ 0.01
Best-of-N	1.77 $\pm$ 0.39	1.51 $\pm$ 0.03	5.24 $\pm$ 0.26	0.41 $\pm$ 0.01	0.89 $\pm$ 0.03	100.00 $\pm$ 0.00	0.78 $\pm$ 0.00	0.91 $\pm$ 0.00	202.12 $\pm$ 0.10
TDS	3.70 $\pm$ 1.67	1.11 $\pm$ 0.11	5.28 $\pm$ 0.13	0.28 $\pm$ 0.05	0.84 $\pm$ 0.06	51.88 $\pm$ 1.38	0.37 $\pm$ 0.06	0.56 $\pm$ 0.09	204.19 $\pm$ 0.26
SMC	6.25 $\pm$ 4.69	1.35 $\pm$ 0.29	4.79 $\pm$ 0.79	0.29 $\pm$ 0.17	0.92 $\pm$ 0.01	51.98 $\pm$ 1.19	0.39 $\pm$ 0.09	0.67 $\pm$ 0.08	90.12 $\pm$ 0.31

Appendix

Table 14: DNA design guided by a continuous property score. The same Activity

+

ATAC task and the same seven configurations as Tab. 1 , with the gated reward of Eq. ( 10 ) replaced by a weighted sum of the two property scores standardized on frozen-prior samples,

R_{\lambda}=\lambda z_{\text{act}}+(1-\lambda)z_{\text{ATAC}}

. No acceptance threshold enters the reward, and nothing was re-tuned. Joint SR is scored against the unchanged canonical criteria.

\lambda

weights the first objective and is part of the reward, not a sampler setting: at one

\lambda

every method optimizes the same

R_{\lambda}

. Because

z

is in units of the prior’s own standard deviation,

\lambda=0.5

means equal weight in prior spread, not equal importance. Blocks are different objective functions and are not comparable to each other. Guardrails are reported without ranking.

N=640

per seed, mean

\pm

s.d. over three seeds.

Method	Joint SR (%) $\uparrow$	$\Delta\Delta G$ $\uparrow$		SeqRec $\uparrow$		Uniq. (%)	scRMSD (%)	pLDDT (%)	Time (ms)
		Median	Top-10	Median	Top-10				Time (ms)
$\lambda=0.25$ : SeqRec-leaning
Pretrained	4.04 $\pm$ 0.30	-0.45 $\pm$ 0.00	0.49 $\pm$ 0.03	0.44 $\pm$ 0.00	0.48 $\pm$ 0.00	99.67 $\pm$ 0.05	93.55 $\pm$ 0.11	87.98 $\pm$ 0.11	17.36 $\pm$ 0.04
Best-of-N	15.30 $\pm$ 0.19	0.03 $\pm$ 0.01	0.80 $\pm$ 0.02	0.50 $\pm$ 0.00	0.52 $\pm$ 0.00	99.15 $\pm$ 0.16	93.36 $\pm$ 0.16	86.46 $\pm$ 0.16	160.54 $\pm$ 0.12
TDS	3.84 $\pm$ 0.00	-0.47 $\pm$ 0.04	0.61 $\pm$ 0.11	0.45 $\pm$ 0.00	0.47 $\pm$ 0.00	21.70 $\pm$ 0.72	95.25 $\pm$ 0.42	89.34 $\pm$ 0.15	126.66 $\pm$ 0.03
SMC	6.60 $\pm$ 0.43	-0.40 $\pm$ 0.02	0.42 $\pm$ 0.01	0.45 $\pm$ 0.00	0.48 $\pm$ 0.00	23.65 $\pm$ 0.80	93.47 $\pm$ 0.62	86.98 $\pm$ 0.14	84.37 $\pm$ 0.84

Appendix

Table 15: Protein design guided by a continuous property score. The same

\Delta\Delta G

+

SeqRec task and the same seven configurations as Tab. 2 , with the gated reward replaced by

R_{\lambda}=\lambda z_{\Delta\Delta G}+(1-\lambda)z_{\text{SeqRec}}

on frozen-prior statistics. No acceptance threshold enters the reward, and nothing was re-tuned. Joint SR is scored against the unchanged

\Delta\Delta G>0

and SeqRec

>0.55

\lambda

weights

\Delta\Delta G

and is part of the reward, not a sampler setting. Because

z

is in units of the prior’s own standard deviation,

\lambda=0.5

means equal weight in prior spread, not equal importance. Blocks are different objective functions and are not comparable to each other. Guardrails are reported without ranking.

N=128

per backbone over 12 backbones, mean

\pm

s.d. over three seeds.

Explore similar work

Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design
May 28, 2026Sven Gutjahr, Riccardo De Santi, Luca Schaufelberger +2Constrained Generative Modeling Molecular Optimization
Department of Computer Science, ETH Zurich · ETH AI Center · NCCR Catalysis, Switzerland +1
ParetoPilot: Zero-Surrogate Offline Multi-Objective Optimization via Infer-Perturb-Guide Diffusion
Jun 3, 2026Ruiqing Sun, Sen Yang, Dawei Feng +3Diffusion Guidance Multi-Objective Optimization
College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China · Bioinformatics Center of AMMS, Beijing 100080, China
Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search
Aug 16, 2026Zhongwei Yu, Yan Song, Xue Yan +9Bayesian Optimization Large Language Model-Guided Optimization
The Hong Kong University of Science and Technology (GZ) · University College London · AI Lab, The Yangtze River Delta +3

May 28, 2026, cs.LGJ/K move · Enter open · S save

Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design

Sven Gutjahr, Riccardo De Santi, Luca Schaufelberger, Kjell Jorner+1

Department of Computer Science, ETH Zurich · ETH AI Center · NCCR Catalysis, Switzerland+1

Constrained Generative Modeling Molecular Optimization Generative Modeling Flow-Based Generative Modeling

Open paper AskPDF arXiv

Adapting generative foundation models, in particular diffusion and flow models, to optimize given reward functions (e.g., binding affinity) while satisfying constraints (e.g., molecular synthesizability) is fundamental for their adoption in real-world scientific discovery applications such as molecular design or protein engineering. While recent works have introduced scalable methods for reward-guided fine-tuning of such models via reinforcement learning and control schemes, it remains an open problem how to algorithmically trade-off reward maximization and constraint satisfaction in a reliable and predictable manner. Motivated by this challenge, we first present a rigorous framework for Constrained Generative Optimization, which brings an optimization viewpoint to the introduced adaptation problem and retrieves the relevant task of constrained generation as a sub-case. Then, we introduce Constrained Flow Optimization (CFO), an algorithm that automatically and provably balances reward maximization and constraint satisfaction by reducing the original problem to sequential fine-tuning via established, scalable methods. We provide convergence guarantees for constrained generative optimization and constrained generation via CFO. Ultimately, we present an experimental evaluation of CFO on both synthetic, yet illustrative, settings, and a molecular design task. Across these evaluations, CFO achieves consistent increases in reward while ensuring high constraint satisfaction, showcasing its practical utility for constrained generative optimization.

Abstract

Explore similar work

Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design

ParetoPilot: Zero-Surrogate Offline Multi-Objective Optimization via Infer-Perturb-Guide Diffusion

Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search