Organizations: School of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China · School of Computer Science and Technology, Anhui University, Hefei, Anhui, China · State Key Laboratory for Novel Software Technology at Nanjing University, School of Computer Science, Nanjing University, Nanjing, Jiangsu, China
RNA design aims to identify sequences that fold into specified secondary structures. Existing methods formulate the task as target-specific search or conditional generation. However, natural RNA evolution proceeds through sequence variation and selection, with compensatory substitutions, whereas these methods do not explicitly model this process. To address this limitation, we propose a two-stage framework comprising RNA Inverse-Folding Flow (RNA-IFlow) and RNA-IFlow-RL. RNA-IFlow uses structure-conditioned Dirichlet Flow Matching to model coordinated variation across the sequence, while RNA-IFlow-RL maps the learned flow to a pairing-preserving finite policy and refines it with thermodynamic feedback. Our framework achieves leading performance on multiple benchmarks, reaching 85.19% Pass@1 on Rfam-27. Further analyses reveal thermodynamic gains, policy dynamics, and robustness across settings. Our work couples coordinated variation with thermodynamic selection, offering a novel paradigm for RNA design.
Figures & tables
Figure 1: Overview of the two-stage framework. (a) illustrates the variation–selection motivation. (b) shows RNA-IFlow supervised training. (c) shows RNA-IFlow-RL training and inference.
Figure 2: Post-training dynamics and sensitivity analysis. (a) shows reward and P@8 changes during post-training. (b,c) show shifts in target-probability and NED distributions. (d,e) show mean P@8 ± SD across three seeds for H and G , together with inference and update times, respectively.
Figure 3: Continuous-flow and finite-policy sequence evolution. (a) shows sequence uncertainty, prediction confidence, and the proportion of legal target pairs over normalized flow time. (b) compares scheduled (blue) and actual (orange) nucleotide updates across policy steps. (c) compares matched RNA-IFlow and RNA-IFlow-RL trajectories; red boxes mark differences from the initial sequence.
Figure 4: This figure compares Anemone designs (214 nt). Scores and recovery use full sequences to evaluate. In the visualization of secondary structure, red bases mark differences from the reference, while green, orange, and dashed gray bonds denote recovered, alternative, and missing pairs.
Appendix figures & tables37 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: This figure compares candidate budgets on Eterna100-v2. Panel (a) shows uMFE coverage, panels (b,c) show the best target probability and NED, and panel (d) shows distinct valid sequences. Curves use nested candidate prefixes.
Figure 6: This figure analyzes training-data composition and coverage. Panel (a) compares equal-size training mixtures, while panel (b) relates composition to quality (left) and fixed-exposure coverage to diversity (right). Unique samples denote distinct target structures.
Figure 7: This figure compares quality and cost under the recorded generation and native-search protocols. Panel (a) shows runtime, panel (b) shows uMFE success, and panels (c,d) show target probability and NED. Boxes show quartiles and diamonds denote means.
Method
Total parameters
Millions
Trained parameters
RNA-Design-LM SL
357921408
357.92
-
RNA-Design-LM SL+RL
357921408
357.92
-
GoForth
59392004
59.39
-
DRAG
37285
0.04
-
RNAinverse-pf
-
-
-
RNA-IFlow
87548613
87.55
86958021
Appendix
Table 3: This table reports model capacity. A dash denotes either no neural parameters for pure search or an unknown historical training mask.
Method
P@1
P@8
MFE@1
MFE@8
Prob.
F1
NED
Div.
RNA-Design-LM SL
0.2633
0.4333
0.2700
0.4433
0.3364
0.7735
0.1694
0.9996
RNA-Design-LM SL+RL
0.5133
0.6367
0.5233
0.6567
0.5256
0.9324
0.0652
0.9783
GoForth
0.3933
0.5700
0.4133
0.5833
0.3499
0.9236
0.0804
0.9862
DRAG
0.3633
0.5133
0.3633
0.5200
0.2391
0.9062
0.1345
0.8029
RNAinverse-pf
0.4367
0.5433
0.4533
0.5700
0.4344
0.6544
0.3625
0.6429
RNA-IFlow (Ours)
0.3033
0.5200
0.3133
0.5367
0.4089
0.8731
0.1017
0.9979
Appendix
Table 4: This table reports complete Eterna100-v2 results for eight returned candidates. Lower NED is better; all other metrics are higher-is-better.
Method
P@1
P@8
MFE@1
MFE@8
Prob.
F1
NED
Div.
RNA-Design-LM SL
0.2633
0.4267
0.2700
0.4333
0.3326
0.7669
0.1702
0.9996
RNA-Design-LM SL+RL
0.5033
0.6133
0.5167
0.6333
0.5165
0.9196
0.0691
0.9812
GoForth
0.3933
0.5667
0.4133
0.5733
0.3435
0.9116
0.0848
0.9858
DRAG
0.3633
0.5133
0.3633
0.5167
0.2376
0.8960
0.1373
0.8063
RNAinverse-pf
0.4433
0.5100
0.4567
0.5267
0.4292
0.6442
0.3594
0.6400
RNA-IFlow (Ours)
0.3000
0.4867
0.3100
0.5067
0.3988
0.8596
0.1099
0.9975
Appendix
Table 5: This table reports complete Eterna100 results for eight returned candidates. Lower NED is better; all other metrics are higher-is-better.
Method
P@1
P@8
MFE@1
MFE@8
Prob.
F1
NED
Div.
RNA-Design-LM SL
0.5185
0.7531
0.5185
0.7531
0.6200
0.9814
0.0267
1.0000
RNA-Design-LM SL+RL
0.8148
0.8642
0.8148
0.8642
0.7765
0.9970
0.0058
1.0000
GoForth
0.6296
0.7284
0.6296
0.7407
0.4878
0.9930
0.0162
1.0000
DRAG
0.7160
0.8272
0.7407
0.8272
0.4218
0.9962
0.0468
0.5170
RNAinverse-pf
0.3827
0.4568
0.3827
0.4568
0.4375
0.4932
0.5076
0.4398
RNA-IFlow (Ours)
0.6543
0.8272
0.6667
0.8395
0.7158
0.9944
0.0104
1.0000
Appendix
Table 6: This table reports complete Rfam-27 results for eight returned candidates. Lower NED is better; all other metrics are higher-is-better.
Method
P@1
P@8
MFE@1
MFE@8
Prob.
F1
NED
Div.
RNA-Design-LM SL
0.5951
0.7256
0.6069
0.7378
0.6418
0.9651
0.0347
0.9999
RNA-Design-LM SL+RL
0.7199
0.7531
0.7356
0.7657
0.7156
0.9808
0.0154
0.9774
GoForth
0.6252
0.7216
0.6440
0.7347
0.5858
0.9756
0.0274
0.9848
RNA-IFlow (Ours)
0.6165
0.7395
0.6339
0.7535
0.6890
0.9755
0.0203
0.9992
RNA-IFlow-RL (Ours)
0.7120
0.7312
0.7299
0.7544
0.7109
0.9783
0.0157
0.9186
Appendix
Table 7: This table reports complete RNAsolo-764 results for eight returned candidates. Lower NED is better; all other metrics are higher-is-better.
Method
Full P@8
755 P@8
Full NED
755 NED
RNA-Design-LM SL
0.7256
0.7223
0.0347
0.0351
RNA-Design-LM SL+RL
0.7531
0.7501
0.0154
0.0156
GoForth
0.7216
0.7183
0.0274
0.0274
RNA-IFlow
0.7395
0.7364
0.0203
0.0205
RNA-IFlow-RL
0.7312
0.7280
0.0157
0.0159
Appendix
Table 8: RNAsolo overlap sensitivity. The 755-target subset excludes the nine exact supervised target-structure overlaps without using model outcomes.
Generator
P@1
P@8
Prob.
NED
Native RNA-IFlow
0.3033
0.5200
0.4089
0.1017
RNA-IFlow-no-RL
0.1233
0.2433
0.1822
0.2399
RNA-IFlow-RL
0.5400
0.6500
0.5398
0.0534
Appendix
Table 10: This table summarizes the policy interface and post-training results on Eterna100-v2.
Axis
Value
P@1
P@8
Prob.
NED
H
1
0.4533
0.6033
0.4821
0.0736
H
2
0.5000
0.6567
0.5312
0.0590
H
4
0.4900
0.6367
0.5258
0.0598
H
8
0.5167
0.6500
0.5424
0.0558
H
16
0.5000
0.6500
0.5317
0.0599
G
2
0.5167
0.6500
0.5312
0.0587
Appendix
Table 11: This table reports complete single-seed policy sensitivity; group size one is the zero-advantage boundary.
Configuration
P@1
P@8
Prob.
NED
H=2,G=8
0.5033±0.0058
0.6511±0.0096
0.5309±0.0063
0.0593±0.0014
H=8,G=8
0.5122±0.0051
0.6578±0.0107
0.5391±0.0043
0.0554±0.0016
H=8,G=4
0.5122±0.0102
0.6544±0.0051
0.5351±0.0023
0.0562±0.0008
H=8,G=16
0.5178±0.0158
0.6578±0.0019
0.5365±0.0016
0.0557±0.0013
Appendix
Table 12: Values are reported as means and sample standard deviations across three repeated sensitivity runs.
G
Median (s)
Minimum (s)
Maximum (s)
2
25.7918
10.5854
34.0818
4
27.4301
10.4608
35.9115
8
39.0918
11.9554
72.1897
16
56.9375
12.3717
302.8546
Appendix
Table 13: This table reports observed group-size update costs on shared GPUs; minimum and maximum values summarize profiling variability.
Steps
P@1
P@8
MFE@8
Prob.
4
0.2800
0.5033
0.5033
0.3991
8
0.2900
0.5133
0.5367
0.4041
16
0.2967
0.5133
0.5367
0.4056
32
0.3000
0.5133
0.5333
0.4095
50
0.3033
0.5200
0.5367
0.4089
Appendix
Table 14: This table reports native-flow integration-step sensitivity on 100 Eterna100-v2 targets.
Updates
P@1
P@8
MFE@8
Prob.
1744
0.5233
0.6567
0.6867
0.5446
2093
0.5333
0.6533
0.6767
0.5364
2442
0.5400
0.6500
0.6733
0.5398
2790
0.5300
0.6500
0.6800
0.5437
Appendix
Table 15: This table reports checkpoint performance during post-training continuation.
Setting
P@1
P@8
Prob.
NED
Div.
Original mixture
0.5133
0.6533
0.5363
0.0555
0.9513
Core-only
0.4867
0.6333
0.5203
0.0616
0.9279
Hard-enriched
0.4900
0.6333
0.5248
0.0610
0.9379
Appendix
Table 16: This table compares matched-size training-data compositions.
Setting
P@1
P@8
Prob.
NED
Div.
1395 unique tasks
0.5000
0.6500
0.5361
0.0590
0.9071
2790 unique tasks
0.5133
0.6267
0.5269
0.0596
0.9175
4143 unique tasks
0.5033
0.6467
0.5367
0.0565
0.9292
Appendix
Table 17: This table reports coverage under a fixed number of target visits.
Setting
P@1
P@8
Prob.
NED
Div.
Lower CE weight
0.5133
0.6433
0.5332
0.0576
0.9487
Higher CE weight
0.5167
0.6467
0.5361
0.0582
0.9517
Lower KL weight
0.5167
0.6533
0.5408
0.0546
0.9413
Higher KL weight
0.5233
0.6433
0.5313
0.0561
0.9400
Appendix
Table 18: This table reports one-axis regularization sensitivity with all other settings fixed.
Setting
P@1
P@8
Prob.
NED
One fresh round
0.5133
0.6633
0.5425
0.0551
Two fresh rounds
0.5167
0.6500
0.5424
0.0558
Fixed behavior snapshot, two rounds
0.5233
0.6533
0.5396
0.0557
Three fresh rounds
0.5100
0.6467
0.5396
0.0558
Fixed behavior snapshot, three rounds
0.5233
0.6600
0.5435
0.0554
Appendix
Table 19: This table reports rollout-freshness and reuse controls.
Method
Return time (s)
With scoring (s)
Timed groups
RNA-Design-LM SL
4.4085
4.7356
600
RNA-Design-LM SL+RL
4.4085
4.6438
600
GoForth
1.3518
1.6502
600
DRAG
14.8637
15.0512
300
RNAinverse-pf
133.5565
133.7930
300
RNA-IFlow
0.8845
1.1684
600
Appendix
Table 20: This table reports time to return eight candidates and time after common scoring. Neural entries use matched resident-model medians, while search rows retain their native timing scope.
K
Pass@K
MFE@K
Prob.
NED
Pair-F1
Diversity
1
0.2633
0.2700
0.2136
0.2762
0.5899
1.0000
2
0.3433
0.3500
0.2618
0.2276
0.6662
1.0000
4
0.4033
0.4100
0.3024
0.1946
0.7313
1.0000
8
0.4333
0.4433
0.3364
0.1694
0.7735
0.9996
16
0.4800
0.4967
0.3719
0.1497
0.8187
0.9992
32
0.5167
0.5467
0.4064
0.1319
0.8539
0.9985
Appendix
Table 21: This table reports RNA-Design-LM SL nested-prefix results from the same ordered candidate set, with each metric aggregated separately.
K
Pass@K
MFE@K
Prob.
NED
Pair-F1
Diversity
1
0.5133
0.5233
0.4238
0.1099
0.8319
1.0000
2
0.5833
0.5900
0.4756
0.0855
0.8847
0.9950
4
0.6200
0.6333
0.5036
0.0743
0.9145
0.9883
8
0.6367
0.6567
0.5256
0.0652
0.9324
0.9783
16
0.6500
0.6800
0.5375
0.0582
0.9493
0.9683
32
0.6600
0.6967
0.5501
0.0530
0.9543
0.9581
Appendix
Table 22: This table reports RNA-Design-LM SL+RL nested-prefix results from the same ordered candidate set, with each metric aggregated separately.
K
Pass@K
MFE@K
Prob.
NED
Pair-F1
Diversity
1
0.3933
0.4133
0.2302
0.1357
0.8096
1.0000
2
0.4633
0.4800
0.2714
0.1101
0.8667
0.9933
4
0.5433
0.5533
0.3276
0.0895
0.9075
0.9900
8
0.5700
0.5833
0.3499
0.0804
0.9236
0.9862
16
0.5933
0.6200
0.3731
0.0744
0.9360
0.9831
32
0.6100
0.6300
0.3894
0.0693
0.9435
0.9793
Appendix
Table 23: This table reports GoForth nested-prefix results from the same ordered candidate set, with each metric aggregated separately.
K
Pass@K
MFE@K
Prob.
NED
Pair-F1
Diversity
1
0.3033
0.3133
0.2534
0.1880
0.6872
1.0000
2
0.3733
0.3900
0.3076
0.1477
0.7766
1.0000
4
0.4600
0.4800
0.3680
0.1224
0.8334
0.9975
8
0.5200
0.5367
0.4089
0.1017
0.8731
0.9979
16
0.5700
0.5967
0.4410
0.0894
0.9020
0.9960
32
0.5933
0.6167
0.4650
0.0818
0.9175
0.9931
Appendix
Table 24: This table reports RNA-IFlow nested-prefix results from the same ordered candidate set, with each metric aggregated separately.
K
Pass@K
MFE@K
Prob.
NED
Pair-F1
Diversity
1
0.5400
0.5433
0.4483
0.0906
0.8527
1.0000
2
0.5867
0.5900
0.4854
0.0748
0.8906
0.9850
4
0.6233
0.6300
0.5127
0.0633
0.9190
0.9683
8
0.6500
0.6733
0.5398
0.0534
0.9396
0.9363
16
0.6633
0.6933
0.5517
0.0499
0.9510
0.9071
32
0.6833
0.7133
0.5626
0.0462
0.9597
0.8772
Appendix
Table 25: This table reports RNA-IFlow-RL nested-prefix results from the same ordered candidate set, with each metric aggregated separately.
Method
uMFE
MFE
Prob.
NED
Pair-F1
Run time (s)
FastDesign
0.4900
0.5267
0.3827
0.3589
0.6623
33.5269
SAMFEO
0.6667
0.6933
0.5283
0.0579
0.9474
43.3045
NEMO
0.2933
0.3167
0.1720
0.2928
0.6530
15.9501
Appendix
Table 26: This table reports native-search performance on Eterna100-v2 with at most 60 seconds per target and seed. Time is the observed mean search time, and all 300 groups contribute to the metrics.
Method
Groups
Timeouts
Empty returns
Mean returned
FastDesign
300
93
93
3.4267
SAMFEO
300
172
0
9.9200
NEMO
300
68
48
0.8400
Appendix
Table 27: This table reports search completion and returned-candidate counts under the same native 60-second protocol. Returned counts describe the final candidate sets.
Method
MFE
uMFE
Budget / source
RNA-IFlow-RL
73
68
At most 10,000 candidates; global stop
RNA-Design-LM SL+RL
74
72
Published 10,000-sample evaluation ( Gautam et al., 2026 )
FastDesign
80
78
Published motif/cube search ( Zhou et al., 2026 )
SAMFEO
77
74
Five-run union, probability objective ( Zhou et al., 2023 )
NEMO
79
77
Five-run union reported by Zhou et al. (2023)
Appendix
Table 28: This table reports Eterna100 large-budget coverage as solved targets out of 100. NEMO counts follow the SAMFEO authors’ reproduction.
Benchmark
Method
MFE
uMFE
Protocol
Eterna100-v2
RNA-IFlow-RL
81
76
Maximum 10,000 candidates
Eterna100-v2
RNA-Design-LM SL+RL
81
79
Published 10,000 samples ( Gautam et al., 2026 )
Rfam-27
RNA-IFlow-RL
24
24
Maximum 10,000 candidates
Rfam-27
RNA-Design-LM SL+RL
24
24
Published 10,000 samples ( Gautam et al., 2026 )
RNAsolo-764
RNA-IFlow-RL
591
585
Maximum 10,000 candidates
Appendix
Table 29: This table reports additional large-budget generator coverage under each source’s original stopping and aggregation protocol.
Method
MFE solved
uMFE solved
Source
FastDesign
611
606
Zhou et al. (2026) , Table 2
SAMFEO
608
602
Zhou et al. (2026) , Table 2
NEMO
609
605
Zhou et al. (2026) , Table 2
Appendix
Table 30: This table reports published RNAsolo-764 search coverage from the FastDesign comparison using the source paper’s native search protocol.
Sequence
Prob.
NED
MFE
uMFE
Group MFE
Group uMFE
Reference sequence
0.1803
0.0367
yes
yes
–
–
RNA-IFlow-RL
0.5178
0.0128
yes
yes
2/8
2/8
RNA-IFlow
0.1257
0.0773
no
no
0/8
0/8
RNA-Design-LM SL+RL
0.0769
0.0297
no
no
0/8
0/8
GoForth
0.0019
0.1477
no
no
0/8
0/8
DRAG
0.0007
0.0447
no
no
0/8
0/8
Appendix
Table 31: This table reports displayed-candidate thermodynamics and group-level hit counts for Anemone. Reference metrics are evaluated independently and do not form a generated K=8 group.
Figure 8: This figure shows additional first-candidate designs, with a recovered target above and a residual uMFE failure below. Green, orange, and dashed gray bonds denote recovered, alternative, and missing pairs, while nucleotide colors denote A/C/G/U in orange/blue/green/purple.
Target
nt
Model
Prob.
NED
uMFE
Ete_19
104
RNA-IFlow
0.0023
0.0647
no
Ete_19
104
RNA-IFlow-RL
0.9467
0.0022
yes
Ete_50
108
RNA-IFlow
5.5166×10−7
0.3343
no
Ete_50
108
RNA-IFlow-RL
0.0006
0.2935
no
Appendix
Table 32: This table reports additional fixed-first-candidate thermodynamics; small nonzero probabilities are retained in scientific notation.
Figure 9: This figure shows frozen-supervised-flow profiles over 12,613 training-pool targets, each with eight valid candidates. Panels (a,b) report target fractions by empirical uMFE success and mean normalized structural distance, respectively.
Figure 10: This figure compares candidate-level target-probability histograms before and after RL. Gray and blue outlines denote the finite policy without RL and RNA-IFlow-RL, while the vertical axis reports the candidate fraction in each probability bin.
Figure 11: This figure shows training-set length distributions. Bars report sample fractions in each length interval, with green and blue denoting supervised and RL training data, respectively.
Sequence
Matching positions
Recovery (%)
Author/player reference
214/214
100.00
RNA-Design-LM SL+RL
87/214
40.65
GoForth
88/214
41.12
DRAG
101/214
47.20
RNA-IFlow
97/214
45.33
RNA-IFlow-RL
114/214
53.27
Appendix
Table 33: This table reports full-length recovery for the displayed Anemone candidates using the same 214-nucleotide reference throughout.
RNA function arises from the coupling of nucleotide sequence and three-dimensional structure, motivating their joint design. Coordinating global folding with nucleotide-level detail remains challenging under limited structural supervision. We introduce La-Ribo, a generative framework for RNA sequence-structure co-design via geometry-latent flow matching. La-Ribo retains a sparse phosphate-sugar--base scaffold and encodes nucleotide identity and local conformation in residue-wise latents. A shared flow network generates both jointly, and an RNA-specific decoder then reconstructs all heavy atoms. To expand supervision, we construct a quality-controlled corpus of 168,561 RNA structures, integrating experimental data with predictions from three folding models, including 10,631 MSA-supported structures generated in this work. La-Ribo improves designability and codesignability over the evaluated baselines across sampling budgets and two refolding models, and the same prior supports scaffold-conditioned inverse folding without additional training.
Runze Ma, Will Hua, Shuangjia Zheng
Shanghai Jiao Tong University · Independent Researcher
We introduce MORAD, an online reinforcement learning framework for backbone-conditioned RNA diffusion models that trains a single shared policy across diverse target backbones. Structure-conditioned RNA inverse design seeks nucleotide sequences compatible with a target three-dimensional backbone, yet existing reinforcement learning approaches either optimize a separate policy for each target backbone or rely on offline preference optimization, leaving online post-training of a reusable backbone-conditioned model largely unexplored. MORAD combines backbone-conditioned group sampling, group-relative reward normalization, and a forward-process diffusion objective. Beyond existing RL rewards that primarily target tertiary structural quality, MORAD jointly optimizes six measurements spanning tertiary geometry, base pairing, ensemble behavior, and sequence composition. To aggregate these heterogeneous objectives despite differences in scale and optimization direction, MORAD maps each measurement to a bounded desirability score and combines them with a weighted geometric mean. Compared with a tertiary-structure-only reward, this multi-objective formulation improves 10 of the 11 evaluation metrics that have a preferred direction. Applied to pretrained RIDE, MORAD improves GDT-TS by 16.0% (from 0.3300 to 0.3827) and pairing MCC by 19.4% (from 0.6110 to 0.7295), while reducing normalized ensemble defect by 27.5% (from 0.3906 to 0.2830). On the test set, MORAD outperforms RiboDiffusion, gRNAde, and RDesign across tertiary structural accuracy, secondary-structure pairing, and thermodynamic quality, establishing a new state of the art in structure-conditioned RNA inverse design.
The inverse design of RNA three-dimensional (3D) structures is crucial for engineering functional RNAs in synthetic biology and therapeutics. While recent deep learning approaches have advanced this field, they are typically optimized and evaluated using native sequence recovery, which is a limited surrogate for structural fidelity, since different sequences can fold into similar 3D structures and high recovery does not necessarily indicate correct folding. To address this limitation, we propose RIDER, an RNA Inverse DEsign framework with Reinforcement learning that directly optimizes for 3D structural similarity. First, we develop and pre-train a GNN-based generative diffusion model conditioned on the target 3D structure, achieving a 9% improvement in native sequence recovery over state-of-the-art methods. Then, we fine-tune the model with an improved policy gradient algorithm using four task-specific reward functions based on 3D self-consistency metrics. Experimental results show that RIDER improves structural similarity by over 100% across all metrics and discovers designs that are distinct from native sequences.