La-Ribo: RNA Co-Design via Geometry-Latent Flow Matching

Runze Ma; Will Hua; Shuangjia Zheng

q-bio.BMOct 8, 2026

La-Ribo: RNA Co-Design via Geometry-Latent Flow Matching

Authors: Runze Ma, Will Hua, Shuangjia Zheng

Organizations: Shanghai Jiao Tong University · Independent Researcher

Abstract

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.

Figures & tables

Figure 1: Overview of La-Ribo. (a) Each residue is represented by an explicit P/C4’/glycosidic-N scaffold (blue) and an encoded 16-dimensional latent (red). (b) A shared flow network jointly generates states with modality-specific schedules. (c) The frozen decoder predicts nucleotide identity, a scaffold-to-sugar rotation, and torsions, from which the atom builder builds all heavy atoms.

		Designability			Codesignability
Method	Steps	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	#Clust. $\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	#Clust. $\uparrow$
RNA-FrameFlow	50	$25.17{\scriptstyle\,\pm\,1.09}$	$36.61{\scriptstyle\,\pm\,0.19}$	$24.00{\scriptstyle\,\pm\,1.73}$	–	–	–
	100	$26.61{\scriptstyle\,\pm\,1.18}$	$39.67{\scriptstyle\,\pm\,0.33}$	$27.00{\scriptstyle\,\pm\,2.65}$	–	–	–
	200	$26.17{\scriptstyle\,\pm\,1.76}$	$38.44{\scriptstyle\,\pm\,1.84}$	$26.00{\scriptstyle\,\pm\,1.00}$	–	–	–
	400	$26.89{\scriptstyle\,\pm\,1.69}$	$38.89{\scriptstyle\,\pm\,1.69}$	$27.00{\scriptstyle\,\pm\,3.61}$	–	–	–
RiboFlow-Exp	50	$22.28{\scriptstyle\,\pm\,0.63}$	$30.44{\scriptstyle\,\pm\,0.54}$	$19.33{\scriptstyle\,\pm\,4.04}$	$19.22{\scriptstyle\,\pm\,0.35}$	$24.94{\scriptstyle\,\pm\,0.10}$	$15.33{\scriptstyle\,\pm\,2.52}$

Table 1: Unconditional RNA generation at 50–400 steps. Mean

\pm

standard deviation over three 600-RNA campaigns; bold marks the best mean at each step count.

Figure 2: Latent interventions with a fixed scaffold. (a,b) compare posterior-mean, zero, and shuffled latents; (c) shows atom displacement from a separate one-residue latent perturbation.

Autoencoder	Flow	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	scRMSD $\downarrow$	scTM $\uparrow$
RNA-FrameFlow		$26.17{\scriptstyle\,\pm\,1.76}$	$31.56{\scriptstyle\,\pm\,2.10}$	$38.44{\scriptstyle\,\pm\,1.84}$	$11.47{\scriptstyle\,\pm\,0.29}$	$0.413{\scriptstyle\,\pm\,0.008}$
RiboFlow-Exp		$20.50{\scriptstyle\,\pm\,0.73}$	$25.11{\scriptstyle\,\pm\,0.42}$	$30.06{\scriptstyle\,\pm\,0.69}$	$12.73{\scriptstyle\,\pm\,0.22}$	$0.408{\scriptstyle\,\pm\,0.003}$
VAE	Base	$25.78{\scriptstyle\,\pm\,0.92}$	$29.83{\scriptstyle\,\pm\,2.18}$	$33.67{\scriptstyle\,\pm\,1.88}$	$13.51{\scriptstyle\,\pm\,0.38}$	$0.374{\scriptstyle\,\pm\,0.004}$
VAE	Tri	$\mathbf{30.72}{\scriptstyle\,\pm\,1.39}$	$\mathbf{36.17}{\scriptstyle\,\pm\,0.76}$	$43.44{\scriptstyle\,\pm\,0.54}$	$11.74{\scriptstyle\,\pm\,0.17}$	$0.433{\scriptstyle\,\pm\,0.004}$
E-VAE	Base	$25.50{\scriptstyle\,\pm\,1.20}$	$29.67{\scriptstyle\,\pm\,1.33}$	$34.89{\scriptstyle\,\pm\,1.13}$	$12.66{\scriptstyle\,\pm\,0.14}$	$0.400{\scriptstyle\,\pm\,0.002}$
E-VAE	Tri	$30.17{\scriptstyle\,\pm\,1.36}$	$35.22{\scriptstyle\,\pm\,1.11}$	$\mathbf{44.06}{\scriptstyle\,\pm\,1.49}$	$\mathbf{10.82}{\scriptstyle\,\pm\,0.15}$	$\mathbf{0.444}{\scriptstyle\,\pm\,0.006}$

Table 2: Autoencoder corpus

\times

flow architecture at 200 steps. VAE is trained on the full corpus, E-VAE on its experimental subset; all four flows use experimental structures only. Mean

\pm

standard deviation over three 600-RNA campaigns; RNA-FrameFlow and RiboFlow-Exp are references.

Figure 3: Length-resolved La-Ribo-Tri success at 200 steps for one 600-RNA campaign (50 RNAs per length). Error bars show 95% Wilson intervals.

		Designability			Codesignability
Model	Interval	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$
La-Ribo-Base	–	$38.22{\scriptstyle\,\pm\,1.27}$	$43.44{\scriptstyle\,\pm\,0.48}$	$53.00{\scriptstyle\,\pm\,0.67}$	$\mathbf{32.56}{\scriptstyle\,\pm\,2.25}$	$\mathbf{41.28}{\scriptstyle\,\pm\,1.84}$	$56.72{\scriptstyle\,\pm\,1.78}$
La-Ribo-Tri4	4	$37.33{\scriptstyle\,\pm\,2.03}$	$45.00{\scriptstyle\,\pm\,1.92}$	$55.33{\scriptstyle\,\pm\,1.36}$	$25.17{\scriptstyle\,\pm\,0.59}$	$36.67{\scriptstyle\,\pm\,1.21}$	$52.67{\scriptstyle\,\pm\,1.59}$
La-Ribo-Tri3	3	$38.50{\scriptstyle\,\pm\,2.09}$	$44.00{\scriptstyle\,\pm\,1.89}$	$56.00{\scriptstyle\,\pm\,1.41}$	$26.83{\scriptstyle\,\pm\,0.60}$	$36.50{\scriptstyle\,\pm\,1.15}$	$52.00{\scriptstyle\,\pm\,1.53}$
La-Ribo-Tri	2	$\mathbf{39.11}{\scriptstyle\,\pm\,2.12}$	$\mathbf{48.39}{\scriptstyle\,\pm\,2.08}$	$\mathbf{58.83}{\scriptstyle\,\pm\,1.48}$	$32.06{\scriptstyle\,\pm\,0.75}$	$39.94{\scriptstyle\,\pm\,1.26}$	$\mathbf{57.89}{\scriptstyle\,\pm\,1.71}$

Table 3: Triangle-update interval at 200 steps. Interval counts blocks between pair updates; Base keeps pair features fixed. Mean

\pm

standard deviation over three 600-RNA campaigns.

Figure 4: Local geometry of La-Ribo-Tri (gray) and experimental RNA (blue; RNASolo and RhoFold PDB). (a–c) compare C4 ′ distance, angle, and dihedral; (d) shows generated-minus-experimental pseudotorsion density. JSD is in bits.

	Sequence statistics		Mean of eight			Best of eight
Method	Recovery $\uparrow$	Unique $\uparrow$	$\mathrm{[email protected]}\uparrow$	scRMSD $\downarrow$	scTM $\uparrow$	$\mathrm{[email protected]}\uparrow$	scRMSD $\downarrow$	scTM $\uparrow$
gRNAde	$41.69{\scriptstyle\,\pm\,0.13}$	$6.14{\scriptstyle\,\pm\,0.02}$	$7.83{\scriptstyle\,\pm\,0.31}$	$16.39{\scriptstyle\,\pm\,0.03}$	$\mathbf{0.258}{\scriptstyle\,\pm\,0.0011}$	$11.18{\scriptstyle\,\pm\,0.70}$	$13.60{\scriptstyle\,\pm\,0.16}$	$0.289{\scriptstyle\,\pm\,0.0029}$
NA-MPNN	$\mathbf{42.65}{\scriptstyle\,\pm\,0.02}$	$7.22{\scriptstyle\,\pm\,0.06}$	$6.68{\scriptstyle\,\pm\,0.16}$	$16.68{\scriptstyle\,\pm\,0.05}$	$0.248{\scriptstyle\,\pm\,0.0007}$	$11.78{\scriptstyle\,\pm\,0.35}$	$13.65{\scriptstyle\,\pm\,0.17}$	$0.288{\scriptstyle\,\pm\,0.0006}$
RiboFlow-Mix	$32.14{\scriptstyle\,\pm\,0.20}$	$6.96{\scriptstyle\,\pm\,0.01}$	$4.12{\scriptstyle\,\pm\,0.09}$	$18.62{\scriptstyle\,\pm\,0.05}$	$0.192{\scriptstyle\,\pm\,0.0011}$	$9.02{\scriptstyle\,\pm\,0.35}$	$13.75{\scriptstyle\,\pm\,0.24}$	$0.219{\scriptstyle\,\pm\,0.0008}$
La-Ribo-Base	$34.43{\scriptstyle\,\pm\,0.06}$	$\mathbf{7.67}{\scriptstyle\,\pm\,0.02}$	$7.95{\scriptstyle\,\pm\,0.09}$	$16.36{\scriptstyle\,\pm\,0.15}$	$0.244{\scriptstyle\,\pm\,0.0011}$	$14.24{\scriptstyle\,\pm\,0.35}$	$\mathbf{11.91}{\scriptstyle\,\pm\,0.21}$	$0.309{\scriptstyle\,\pm\,0.0015}$
La-Ribo-Tri	$34.82{\scriptstyle\,\pm\,0.10}$	$7.62{\scriptstyle\,\pm\,0.02}$	$\mathbf{8.84}{\scriptstyle\,\pm\,0.13}$	$\mathbf{15.90}{\scriptstyle\,\pm\,0.17}$	$0.252{\scriptstyle\,\pm\,0.0004}$	$\mathbf{14.84}{\scriptstyle\,\pm\,0.70}$	$12.11{\scriptstyle\,\pm\,0.13}$	$\mathbf{0.313}{\scriptstyle\,\pm\,0.0020}$

Table 4: Inverse folding on 1,002 experimental validation scaffolds, mean

\pm

sample standard deviation over three independently seeded evaluations. Mean-of-eight averages candidates; best-of-eight uses one candidate for strict success. Rates are percentages; Unique counts distinct candidates (of eight); scRMSD is in Å.

Figure 5: Sampling sensitivity. Columns show solver steps, scaffold power

\rho_{B}

, and latent power

\rho_{Z}

; top/bottom rows show marginal strict

\mathrm{[email protected]}

designability/codesignability.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: La-Ribo backbones (40–130 nt, grey) overlaid with refolds of the best of eight gRNAde sequences (top) and the co-designed sequence (bottom). Numbers: C4 ′ scRMSD (Å).

Source	Type	Structures
RNASolo	Experimental	5,772
RhoFold subset	Experimental	3,268
OpenFold3 Distillation	Synthetic	125,833
NuFold Distillation	Synthetic	23,057
trRosettaRNA2 Distillation	Synthetic	10,631
Total	Experimental + Synthetic	168,561

Appendix

Table 5: Eligible RNA structures by source after length and valid-frame filtering. RNASolo and the RhoFold subset are experimental; other sources are synthetic.

Quantity	Shape	Definition and role
Sequence $S$	$N$	Canonical nucleotide identities $s_{i}\in\{A,C,G,U\}$ .
Heavy-atom coordinates $X$	$N\times 37\times 3$	Atom37-style coordinates; $x_{i}^{a}\in\mathbb{R}^{3}$ denotes atom $a$ in residue $i$ .
Scaffold $B=(b_{i})_{i=1}^{N}$	$N\times 9$	$b_{i}=[x_{i}^{\mathrm{P}};x_{i}^{\mathrm{C4^{\prime}}};x_{i}^{\nu_{i}}]$ , with $\nu_{i}=\mathrm{N9}$ for A/G and $\mathrm{N1}$ for C/U.
Latent representation $Z$	$N\times 16$	Residue-wise latent inferred by $E_{\phi}(S,X,B)$ ; it complements $B$ with nucleotide identity and local atomistic information.
Canonical sugar frame $R_{i}^{c}$	$N\times 3\times 3$	$\mathcal{F}(x_{i}^{\mathrm{C4^{\prime}}},x_{i}^{\mathrm{O4^{\prime}}},x_{i}^{\mathrm{C3^{\prime}}})$ , centered at $x_{i}^{\mathrm{C4^{\prime}}}$ .
Torsion targets	$N\times 10\times 2$	Ten RNA dihedrals represented as normalized sine–cosine pairs and used to supervise $U_{i}$ .

Appendix

Table 6: Prepared geometry and atom features for an RNA of length

N

; coordinates are in Å.

Figure 7: Local geometry by corpus source. Rows show the pooled corpus and individual sources; columns show C4 ′ distance, angle, dihedral, and joint

(\eta,\theta)

density. In the pooled row, blue and red outlines distinguish experimental and synthetic structures. Histograms are normalized within each cohort; density panels share a color scale.

Figure 8: Length distributions of 168,561 eligible RNAs, pooled (top) and by source. Histograms are row-normalized; labels report the fraction above 160 nt. Gray, blue, and red denote pooled, experimental, and synthetic structures.

Setting	Value
Optimizer	AdamW , $\beta=(0.9,0.999)$
Learning rate	$10^{-4}$
Weight decay	$10^{-2}$
Epochs	100
Batch size	24 max (length-dependent)
Gradient clipping	1.0

Appendix

Table 7: Scaffold-conditioned autoencoder hyperparameters.

Setting	Value
Optimizer	AdamW , $\beta=(0.9,0.999)$
Learning rate	$10^{-4}$
Weight decay	$10^{-2}$
Epochs	100
Batch size	24 max (length-dependent)
Gradient clipping	1.0

Appendix

Table 8: Geometry–latent flow hyperparameters and default sampling settings.

Figure 9: Base and Tri flow architectures. Both use a 12-block trunk to predict scaffold and latent velocities. La-Ribo-Base keeps pair features fixed as attention biases; La-Ribo-Tri updates them every two blocks using token-to-pair projections and triangle multiplicative updates.

Index	Atom quartet	Standard relation
1	$\mathrm{C5^{\prime}}-\mathrm{C4^{\prime}}-\mathrm{C3^{\prime}}-\mathrm{C2^{\prime}}$	$\delta$ shifted ( $\mathrm{C2^{\prime}}$ for $\mathrm{O3^{\prime}}$ )
2	$\mathrm{C3^{\prime}}-\mathrm{C4^{\prime}}-\mathrm{O4^{\prime}}-\mathrm{C1^{\prime}}$	$\nu_{4}$
3	$\mathrm{C4^{\prime}}-\mathrm{O4^{\prime}}-\mathrm{C1^{\prime}}-\nu_{i}$	$\nu_{0}$ shifted ( $\nu_{i}$ for $\mathrm{C2^{\prime}}$ )
4	$\mathrm{C5^{\prime}}-\mathrm{C4^{\prime}}-\mathrm{C3^{\prime}}-\mathrm{O3^{\prime}}$	$\delta$
5	$\mathrm{C3^{\prime}}-\mathrm{C4^{\prime}}-\mathrm{C5^{\prime}}-\mathrm{O5^{\prime}}$	$\gamma$ reversed
6	$\mathrm{C4^{\prime}}-\mathrm{C5^{\prime}}-\mathrm{O5^{\prime}}-\mathrm{P}$	$\beta$ reversed

Appendix

Table 9: Atom-construction torsions and their standard relations. Each quartet defines a reconstruction dihedral; “reversed” reverses its order without changing the angle, and “shifted” replaces terminal atoms. Here

\nu_{i}

follows Equation 1 , and

A_{\mathrm{base}}

\mathrm{C4}

for A/G or

\mathrm{C2}

for C/U.

Model	Latent	Sequence (%) $\uparrow$	Frame ( ∘ ) $\downarrow$	Non-scaffold RMSD (Å) $\downarrow$	P (Å) $\downarrow$	Glycosidic N (Å) $\downarrow$
VAE	posterior	$100.00{\scriptstyle\,\pm\,0.00}$	$1.779{\scriptstyle\,\pm\,0.010}$	$0.08746{\scriptstyle\,\pm\,0.00021}$	$0.08111{\scriptstyle\,\pm\,0.00023}$	$0.04709{\scriptstyle\,\pm\,0.00048}$
VAE	zero	$24.77{\scriptstyle\,\pm\,0.73}$	$16.447{\scriptstyle\,\pm\,0.081}$	$0.77254{\scriptstyle\,\pm\,0.00651}$	$0.64596{\scriptstyle\,\pm\,0.02262}$	$0.12169{\scriptstyle\,\pm\,0.02587}$
VAE	shuffle	$27.54{\scriptstyle\,\pm\,0.02}$	$20.699{\scriptstyle\,\pm\,0.009}$	$0.96503{\scriptstyle\,\pm\,0.00650}$	$0.75054{\scriptstyle\,\pm\,0.00275}$	$0.10439{\scriptstyle\,\pm\,0.00108}$
E-VAE	posterior	$100.00{\scriptstyle\,\pm\,0.00}$	$2.673{\scriptstyle\,\pm\,0.000}$	$0.12248{\scriptstyle\,\pm\,0.00000}$	$0.09940{\scriptstyle\,\pm\,0.00000}$	$0.05380{\scriptstyle\,\pm\,0.00000}$
E-VAE	zero	$24.99{\scriptstyle\,\pm\,0.00}$	$16.910{\scriptstyle\,\pm\,0.000}$	$0.87019{\scriptstyle\,\pm\,0.00000}$	$0.69486{\scriptstyle\,\pm\,0.00000}$	$0.11057{\scriptstyle\,\pm\,0.00000}$
E-VAE	shuffle	$27.58{\scriptstyle\,\pm\,0.21}$	$20.669{\scriptstyle\,\pm\,0.052}$	$0.98181{\scriptstyle\,\pm\,0.00219}$	$0.76289{\scriptstyle\,\pm\,0.00061}$	$0.11122{\scriptstyle\,\pm\,0.00024}$

Appendix

Table 10: Reconstruction under latent interventions.

Scaffold	$d_{Z}$	AA-RMSD $\downarrow$	NS-RMSD $\downarrow$	Frame $\downarrow$	Torsion $\downarrow$	Seq $\uparrow$
$\mathrm{C4^{\prime}}$	16	0.1533 / 0.1444	0.1589 / 0.1498	2.389	2.326	99.999
$\mathrm{P},\mathrm{C4^{\prime}}$	16	0.1234 / 0.1173	0.1304 / 0.1240	2.313	2.132	100.000
$\mathrm{P},\mathrm{C4^{\prime}},\nu_{i}$	8	0.1259 / 0.1198	0.1334 / 0.1267	2.516	2.418	100.000
$\mathrm{P},\mathrm{C4^{\prime}},\nu_{i}$	16	0.1159 / 0.1107	0.1225 / 0.1170	2.673	2.649	100.000
$\mathrm{P},\mathrm{C4^{\prime}},\nu_{i}$	32	0.1267 / 0.1117	0.1227 / 0.1176	2.886	2.891	100.000

Appendix

Table 11: Reconstruction by scaffold and latent width

d_{Z}

using experimental-only training and a common validation subset. Scaffold labels

\mathrm{P}

\mathrm{C4^{\prime}}

, and

\nu_{i}

abbreviate the anchors

x_{i}^{\mathrm{P}}

x_{i}^{\mathrm{C4^{\prime}}}

, and

x_{i}^{\nu_{i}}

. AA/NS denote all-atom/non-scaffold RMSD (unaligned mean/median, Å); Frame is angular error and Torsion is MAE (degrees, averaged over valid residues); Seq is sequence recovery in percent. Bold marks the best geometric value per column.

Model	Steps	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	scRMSD $\downarrow$	scTM $\uparrow$	#Clust. $\uparrow$
La-Ribo-Tri	50	$37.11{\scriptstyle\,\pm\,0.25}$	$45.22{\scriptstyle\,\pm\,1.21}$	$54.06{\scriptstyle\,\pm\,0.35}$	$8.80{\scriptstyle\,\pm\,0.24}$	$0.474{\scriptstyle\,\pm\,0.004}$	$29.00{\scriptstyle\,\pm\,2.65}$
	100	$37.78{\scriptstyle\,\pm\,1.92}$	$46.89{\scriptstyle\,\pm\,2.41}$	$56.89{\scriptstyle\,\pm\,2.22}$	$8.56{\scriptstyle\,\pm\,0.32}$	$0.487{\scriptstyle\,\pm\,0.008}$	$28.33{\scriptstyle\,\pm\,5.51}$
	200	$39.11{\scriptstyle\,\pm\,2.12}$	$48.39{\scriptstyle\,\pm\,2.08}$	$58.83{\scriptstyle\,\pm\,1.48}$	$8.59{\scriptstyle\,\pm\,0.08}$	$0.491{\scriptstyle\,\pm\,0.002}$	$27.67{\scriptstyle\,\pm\,1.15}$
	400	$38.61{\scriptstyle\,\pm\,2.46}$	$48.39{\scriptstyle\,\pm\,2.75}$	$59.33{\scriptstyle\,\pm\,0.93}$	$8.45{\scriptstyle\,\pm\,0.02}$	$0.494{\scriptstyle\,\pm\,0.004}$	$29.33{\scriptstyle\,\pm\,3.79}$
La-Ribo-Tri3	50	$31.17{\scriptstyle\,\pm\,0.17}$	$37.67{\scriptstyle\,\pm\,1.00}$	$49.00{\scriptstyle\,\pm\,0.29}$	$9.54{\scriptstyle\,\pm\,0.26}$	$0.459{\scriptstyle\,\pm\,0.004}$	$26.33{\scriptstyle\,\pm\,2.31}$
	100	$36.50{\scriptstyle\,\pm\,1.86}$	$42.00{\scriptstyle\,\pm\,2.16}$	$52.83{\scriptstyle\,\pm\,2.06}$	$9.06{\scriptstyle\,\pm\,0.34}$	$0.479{\scriptstyle\,\pm\,0.008}$	$26.33{\scriptstyle\,\pm\,5.13}$

Appendix

Table 13: Designability by triangle-update interval. Mean

\pm

standard deviation over three 600-RNA campaigns per setting; rates are percentages and scRMSD is in Å.

Model	Steps	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	$\mathrm{[email protected]}\uparrow$	scRMSD $\downarrow$	scTM $\uparrow$	#Clust. $\uparrow$
La-Ribo-Tri	50	$28.61{\scriptstyle\,\pm\,1.13}$	$36.06{\scriptstyle\,\pm\,1.93}$	$50.83{\scriptstyle\,\pm\,2.09}$	$10.53{\scriptstyle\,\pm\,0.28}$	$0.449{\scriptstyle\,\pm\,0.009}$	$28.00{\scriptstyle\,\pm\,1.00}$
	100	$30.78{\scriptstyle\,\pm\,1.26}$	$39.00{\scriptstyle\,\pm\,1.83}$	$56.11{\scriptstyle\,\pm\,1.95}$	$9.86{\scriptstyle\,\pm\,0.24}$	$0.471{\scriptstyle\,\pm\,0.008}$	$25.33{\scriptstyle\,\pm\,3.21}$
	200	$32.06{\scriptstyle\,\pm\,0.75}$	$39.94{\scriptstyle\,\pm\,1.26}$	$57.89{\scriptstyle\,\pm\,1.71}$	$9.67{\scriptstyle\,\pm\,0.11}$	$0.477{\scriptstyle\,\pm\,0.003}$	$27.33{\scriptstyle\,\pm\,0.58}$
	400	$32.33{\scriptstyle\,\pm\,0.58}$	$40.17{\scriptstyle\,\pm\,1.17}$	$58.11{\scriptstyle\,\pm\,0.84}$	$9.55{\scriptstyle\,\pm\,0.09}$	$0.479{\scriptstyle\,\pm\,0.003}$	$28.00{\scriptstyle\,\pm\,1.00}$
La-Ribo-Tri3	50	$22.83{\scriptstyle\,\pm\,0.93}$	$31.50{\scriptstyle\,\pm\,1.69}$	$46.00{\scriptstyle\,\pm\,1.89}$	$11.32{\scriptstyle\,\pm\,0.30}$	$0.427{\scriptstyle\,\pm\,0.009}$	$25.33{\scriptstyle\,\pm\,1.15}$
	100	$26.67{\scriptstyle\,\pm\,1.09}$	$35.67{\scriptstyle\,\pm\,1.69}$	$51.17{\scriptstyle\,\pm\,1.77}$	$10.11{\scriptstyle\,\pm\,0.25}$	$0.461{\scriptstyle\,\pm\,0.008}$	$23.00{\scriptstyle\,\pm\,3.00}$

Appendix

Table 14: Codesignability by triangle-update interval. Mean

\pm

standard deviation over three 600-RNA campaigns per setting; rates are percentages and scRMSD is in Å.

3D annotation	Cohort	Mean F1	Median F1	Mean MCC	Median MCC
Geometric contacts	Experimental	0.5815	0.6341	0.5727	0.6320
	La-Ribo-Tri	0.5510	0.6023	0.5465	0.6051
DSSR	Experimental	0.6451	0.7000	0.6367	0.7002
	La-Ribo-Tri	0.6056	0.6563	0.5919	0.6568

Appendix

Table 15: RNAfold agreement with geometric-contact and DSSR annotations on RNASolo dataset and 600 La-Ribo-Tri structures. F1 and MCC are summarized per structure.

Metric	Exp	Syn	La-Ribo-Base	La-Ribo-Tri	RNA-FrameFlow	RiboFlow-Mix
Clash $\downarrow$	0.089	0.646	$2.936{\scriptstyle\,\pm\,0.200}$	$1.846{\scriptstyle\,\pm\,0.097}$	$4.010{\scriptstyle\,\pm\,0.261}$	$6.214{\scriptstyle\,\pm\,0.283}$
C3 ′ -endo (%)	83.482	86.167	$85.696{\scriptstyle\,\pm\,0.061}$	$84.744{\scriptstyle\,\pm\,0.067}$	$91.185{\scriptstyle\,\pm\,0.094}$	$83.890{\scriptstyle\,\pm\,0.168}$
C2 ′ -endo (%)	10.327	9.595	$8.667{\scriptstyle\,\pm\,0.058}$	$9.648{\scriptstyle\,\pm\,0.121}$	$6.466{\scriptstyle\,\pm\,0.007}$	$2.636{\scriptstyle\,\pm\,0.088}$
Other pucker (%)	6.191	4.238	$5.636{\scriptstyle\,\pm\,0.080}$	$5.608{\scriptstyle\,\pm\,0.179}$	$2.349{\scriptstyle\,\pm\,0.090}$	$13.474{\scriptstyle\,\pm\,0.200}$
$\chi$ syn (%)	4.358	3.136	$3.592{\scriptstyle\,\pm\,0.031}$	$3.651{\scriptstyle\,\pm\,0.026}$	–	–
$\chi$ anti (%)	95.642	96.864	$96.408{\scriptstyle\,\pm\,0.031}$	$96.349{\scriptstyle\,\pm\,0.026}$	–	–

Appendix

Table 16: Atomistic geometry of generated structures at 200 steps against the experimental (Exp) and synthetic (Syn) subsets of the training corpus. La-Ribo values are mean

\pm

sample standard deviation over three 600-RNA campaigns; pucker and

\chi

are population percentages over valid residues; planarity and contact distances are in Å.

Cohort	Mean $\mathrm{TM}_{\mathrm{train}}$	$\mathrm{TM}_{\mathrm{train}}\geq 0.8$ (%)	Mean $\mathrm{TM}_{\mathrm{exp}}$	Near-copy (%)
Validation partition (held-out)	0.785	67.6	0.873	12.7
RiboFlow-Mix	0.541	20.6	0.573	14.7
La-Ribo-Base	0.623	31.1	0.625	14.9
La-Ribo-Tri	0.644	37.8	0.659	16.1

Appendix

Table 17: Proximity to the training partition at 200 steps.

\mathrm{TM}_{\mathrm{train}}

and

\mathrm{TM}_{\mathrm{exp}}

are maxima over the training partition and over all experimental structures, respectively. Near-copy requires

\mathrm{TM}\geq 0.8

, sequence identity

\geq 0.8

, and coverage

\geq 0.8

in both directions against the nearest training neighbour. The validation cohort contains the 1,002 experimentally determined structures held out from all training data and serves as the reference cohort.

Figure 10: Strict designability across modality schedules and four architectures. Rows show 100, 200, and 400 steps; each schedule-pair cell contains 600 RNAs. Panels share a color scale, and black outlines mark maxima.

Figure 11: Strict codesignability on the schedule grid of Figure 10 . Panels share a color scale, and black outlines mark maxima.

Factor	Level	Designability $\uparrow$	Codesignability $\uparrow$
Solver steps $K$	100	31.90	25.01
	200	33.18	26.07
	400	33.84	26.67
Scaffold power $\rho_{B}$	0.50	31.03	25.08
	0.70	33.23	25.82
	0.85	33.48	26.04

Appendix

Table 18: Marginal strict

\mathrm{[email protected]}

success by sampling factor, averaged over the remaining grid settings. Each setting has 600 RNAs; rates are percentages.

Figure 12: Generation time for 600 RNAs by solver steps, excluding inverse folding, refolding, and scoring. La-Ribo uses eight A800 GPUs; RNA-FrameFlow time is throughput-normalized. Timing scopes differ; steps are categorical and time is logarithmic.

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Molecular Generation Conditional Generation

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The design of RNA molecules that interact with specific proteins is a critical challenge in experimental and computational biology. Despite recent progress in natural language modeling and deep learning-based protein design, there remains significant room to improve the frequency of successful interactions and the authenticity of generated sequences for functional applications. In this work, we frame conditional RNA sequence generation as a multi-stage alignment problem, introducing Moirain: a suite of models optimized via multimodal supervised fine-tuning (SFT) and Direct Preference Optimization (DPO). Our approach begins with large-scale pretraining on diverse RNA corpora to capture the fundamental grammars of sequence plausibility. To achieve target-specific generation, we employ a multimodal SFT architecture that conditions RNA synthesis on protein structural and sequential features. Finally, we leverage DPO to refine the model using synthetic interaction data: taking advantage of DPO's unique ability to navigate non-aligned preference spaces, we improve functional fitness without collapsing the learned natural distribution. Extensive evaluation of the Moirain series (Moirain-Base, -Multi, and -DPO) demonstrates that our framework consistently produces novel, diverse, and biologically plausible RNA sequences with superior binding affinities compared to existing baselines.

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