GOLD: Geometric Optimized Latent Diffusion for Structure-Aware RNA Inverse Folding

Qi Si; Xuyang Liu; Penglei Wang; Shuo Su; Limei Han; Mengzhu Li; Xin Guo; Yuan Qi

cs.AIOct 16, 2026

GOLD: Geometric Optimized Latent Diffusion for Structure-Aware RNA Inverse Folding

Authors: Qi Si, Xuyang Liu, Penglei Wang, Shuo Su, Limei Han, Mengzhu Li, Xin Guo, Yuan Qi,

Organizations: Shanghai Academy of Artificial Intelligence for Science · School of Biomedical Engineering, Shanghai Jiao Tong University · Community Science Department, Kuaishou · Artificial Intelligence Innovation and Incubation Institute, Fudan University ·

Abstract

Designing RNA sequences that fold into specific 3D structures is a fundamental challenge in therapeutics. Current RNA inverse folding methods typically condition on 3D backbone coordinates but the generation is limited to 1D discrete sequences. This ignores the continuous side-chain orientations, which are essential for overall structural stability. To address this issue, we explicitly introduce side-chain geometry into the RNA generative process. Unlike co-design frameworks that diffuse across separate raw spaces, we propose Geometric Optimized Latent Diffusion (GOLD), which project sequence and structure into a unified latent manifold. GOLD employs a novel GeoVAE to elegantly integrate discrete RNA sequences with continuous side-chain angles. By mapping these modalities into a single, smooth latent manifold, GOLD naturally facilitates a synergistic co-diffusion process. To enhance structural validity, we further introduce a training-free, gradient-guided sampling mechanism. By decoding the generated sequence probabilities and side-chain geometries into structures during the sampling process, we compute analytical gradients from physical constraints. This dynamic feedback actively guides the generated sequence to a physically stable state. Extensive experiments validate the superiority of GOLD, achieving state-of-the-art performance across sequence recovery, secondary structure validity, and 3D foldability metrics. Our code and data are publicly available at https://github.com/darkflash03/GOLD.

Figures & tables

Figure 1: RNA geometry. The backbone establishes local frames ( $\mathbf{R}_{bb}$ ), while the side-chain orientation is governed by the glycosidic torsion angle ( $\chi\in\mathrm{SO}(2)$ ). Modeling this angle in 3D space helps identify potential steric clashes between rigid base planes.

Figure 2: GOLD architecture for RNA inverse folding task. GOLD first encodes RNA sequences and structures into a unified latent space using an rotation aware (SO(2)) encoder, then decodes the latent embeddings into the raw space. Subsequently, a score-based diffusion model, enhanced by a geometric vector perceptron module, is employed in the latent space for RNA generation. During inference, GOLD utilizes an energy-based guidance mechanism to generate desired RNA samples.

GOLD Benchmark (In-Distribution)
Method	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	RMSD (Å, $\downarrow$ )
Method	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	RhoFold	AlphaFold3
PiFold	$0.4123\pm 0.0354$	$0.6184\pm 0.0648$	$17.26\pm 3.56$	$18.73\pm 4.27$
RDesign	$0.4430\pm 0.0326$	$0.6751\pm 0.1106$	$14.65\pm 4.36$	$15.12\pm 3.85$
gRNAde	$0.5453\pm 0.0873$	$0.6450\pm 0.1183$	$15.38\pm 4.84$	$16.10\pm 4.37$
RiboDiffusion	$0.5148\pm 0.0574$	$0.6948\pm 0.0846$	$13.07\pm 3.19$	$13.89\pm 3.92$

Table 1: Performance comparison of 3D RNA inverse folding methods. Evaluation is conducted on the internal GOLD Benchmark and the external CASP15 targets. Results are reported as mean

\pm

standard deviation over five random seeds.

Method	Torsion $\chi$	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	RhoFold RMSD (Å, $\downarrow$ )
SOLD	$\times$	$0.5843\pm 0.0635$	$0.7366\pm 0.0983$	$12.61\pm 2.79$
GOLD (Seq-only)	$\times$	$0.5897\pm 0.0346$	$0.7402\pm 0.1036$	$12.74\pm 2.93$
GOLD (Base)	$\checkmark$	$\mathbf{0.6249\pm 0.0283}$	$\mathbf{0.7785\pm 0.0782}$	$\mathbf{11.99\pm 2.84}$

Table 2: Ablation of explicit sequence–torsion modeling on the GOLD Benchmark. All methods are evaluated without gradient guidance.

Variant	Angle MSE ( $\downarrow$ )	Coord MSE ( $\downarrow$ )	KAE (Å, $\downarrow$ )
w/o $\mathcal{L}_{\mathrm{angle}}$	$0.0546$	$0.0388$	$0.2802$
w/o $\mathcal{L}_{\mathrm{coord}}$	$0.0136$	$0.1611$	$0.6812$
Full GeoVAE	$\mathbf{0.0109}$	$\mathbf{0.0287}$	$\mathbf{0.2466}$

Table 3: Ablation of geometric supervision losses in GeoVAE on the GOLD Benchmark.

Model Variant	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	RMSD (Å, $\downarrow$ )
Model Variant	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	RhoFold	AlphaFold3
GOLD (w/o FM)	$0.6217$	$0.7792$	$11.23$	$12.58$
GOLD (w/ Evo2)	$0.6302$	$0.7922$	$10.85$	$12.40$
GOLD (w/ RNA-FM)	$\mathbf{0.6380}$	$\mathbf{0.8186}$	$\mathbf{10.65}$	$\mathbf{12.31}$

Table 4: Ablation study on Foundation Model (FM) representation alignment.

Guidance Setup	Weights		Seq Recovery ( $\uparrow$ )	SS Validity ( $\uparrow$ )	Clash Score ( $\downarrow$ )
Guidance Setup	$\omega_{ss}$	$\omega_{clash}$	Seq Recovery ( $\uparrow$ )	SS Validity ( $\uparrow$ )	Clash Score ( $\downarrow$ )
Base (No Guidance)	$0.0$	$0.0$	$0.6249$	$0.9040$	$4.51$
SS Guidance Only	$1.0$	$0.0$	$0.6267$	$0.9343$	$4.32$
	$2.0$	$0.0$	$0.6264$	$0.9356$	$4.43$
	$3.0$	$0.0$	$0.6268$	$\mathbf{0.9382}$	$4.38$
Clash Guidance Only	$0.0$	$0.05$	$0.6362$	$0.9012$	$3.11$

Table 5: Ablation study on the training-free Guidance mechanism.

Figure 3: Native structure reconstructions. Left : Unguided (side-chain clashes). Middle : SS-only guided (improved pairing, but residual clashes). Right : Dual-guided (collisions resolved).

Figure 4: AlphaFold3 folding validation for target 6PRV_D . Compared to baselines, the structure designed by GOLD aligns closely with the native ground truth (gray).

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: StructureBuilder and Gradient Flow. The architecture serves as a differentiable routing board, allowing gradients from 2D topological and 3D physical constraints to steer the latent sampling process.

Figure 6: Convergence dynamics of the two-stage training process. (a) Total validation loss of GeoVAE. (b) Total training loss of the Latent Diffusion stage.

Training Stage	Module	Hyperparameter	Value
Stage 1: GeoVAE	Architecture	Node Hidden Dimension ( $d_{model}$ )	256
		Latent Dimension ( $d_{latent}$ )	8
		Encoder/Decoder Layers	4
		Attention Heads	4
		Dropout Rate	0.1
		Pre-trained LLM Embed Dimension (RNA-FM)	640

Appendix

Table 6: Detailed architectural configurations and training hyperparameters for the two-stage generative framework (GeoVAE and Latent Diffusion).

Short-to-Medium Sequences ( $L\leq 100$ )
Method	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	3D RMSD (Å, $\downarrow$ )
Method	Seq Recovery ( $\uparrow$ )	SS Recovery ( $\uparrow$ )	RhoFold	AlphaFold3
PiFold	$0.4237$	$0.6289$	$15.81$	$17.36$
RDesign	$0.4443$	$0.6918$	$13.06$	$13.47$
gRNAde	$0.5440$	$0.6614$	$13.75$	$14.38$
RiboDiffusion	$0.5158$	$0.7061$	$11.56$	$12.41$

Appendix

Table 7: Performance breakdown across different sequence length regimes on the GOLD Benchmark.

PDB ID	Len	Inference Time (s) $\downarrow$			Peak GPU Mem (MB) $\downarrow$
PDB ID	Len	SOLD	GOLD Base	GOLD Dual	SOLD	GOLD Base	GOLD Dual
1A60_A	44	5.12	5.37	7.36	1486	1525	1529
8QO4_A	156	5.34	5.93	9.69	1598	1693	1708
5TC1_R	242	6.28	6.85	11.61	1786	1811	1847
6N7X_R	308	7.05	7.61	14.78	1876	2043	2088

Appendix

Table 8: Inference cost across RNA targets. Time (T) in seconds, Peak Memory (M) in MB.

Figure 7: modality collapse vs. synergistic coupling. Comparison of predicted sequence probability (

\hat{P}_{seq}

) in response to a continuous input-level angular sweep. The Trig-Concat Baseline (left) exhibits an entirely flat response, indicating that the network zeroed out spatial weights early in training. In contrast, the

SO(2)

GeoVAE (right) demonstrates sensitivity to geometric perturbations, proving that its architecture prevents information truncation and forces the synergistic coupling of sequence and geometry.

Figure 8: Structural optimization efficiency. Comparison of the validation KAE descent between the two fusion strategies. The Trig-Concat baseline gets trapped in an optimization plateau near

1.0

Å because it ignores spatial features, whereas the

SO(2)

model demonstrates a smooth and stable structural convergence.

Fusion Strategy	Angle MSE ( $\downarrow$ )	Coord MSE ( $\downarrow$ )	KAE (Å, $\downarrow$ )
Trig-Concat	$0.1416$	$0.3474$	$1.0110$
Fourier–FiLM	$0.0173$	$0.0517$	$0.3659$
$SO(2)$ -aware	$\mathbf{0.0109}$	$\mathbf{0.0287}$	$\mathbf{0.2466}$

Appendix

Table 9: Comparison of sequence–torsion fusion strategies in GeoVAE on the GOLD Benchmark.

Latent Dim ( $d$ )	Seq Recovery ( $\uparrow$ )	KAE ( $\downarrow$ )	Seq Recovery ( $\uparrow$ )	SS Validity ( $\uparrow$ )	Clash Score ( $\downarrow$ )
	GeoVAE (Reconstruction)		LDM (Generation)
$d=4$	0.9998	0.2465	0.5957	0.8747	5.41
$d=8$	0.9996	0.2466	0.6249	0.9040	4.51
$d=16$	0.9997	0.2397	0.6240	0.8955	4.54
$d=32$	0.9999	0.2406	0.6249	0.9033	4.58
$d=64$	0.9998	0.2396	0.6207	0.8924	4.63

Appendix

Table 10: Evaluation of latent dimension (

d

) scaling. We compare the GeoVAE’s upper-bound reconstruction capacity with the actual generative performance of Latent Diffusion Model. To isolate the impact of latent dimensionality, all generative metrics are evaluated on the GOLD Benchmark under the unguided setting . GeoVAE achieves near-perfect local reconstruction even at

d=4

, indicating a low intrinsic physical dimension. However, Latent Diffusion Model generation peaks at

d=8

. Further scaling up to

d=64

plateaus without causing severe performance degradation. Best generative results are highlighted in bold .

Figure 9: Comparative evidence of Partial Posterior Collapse. (a) The KL divergence loss remains stable across 80 epochs even when channel capacity is scaled

d=8

to 64. (b) Comparative analysis of the sorted empirical variance of latent means (

\mu(x)

). The main plot provides a zoomed-in view of the active dimensions, revealing that the variance profile of the over-parameterized

d=64

model perfectly mirrors the intrinsic active dimensions of the baseline

d=8

model. This confirms that all remaining redundant channels collapse to zero (red dashed line). A zero variance of encoded means indicates that the encoder outputs a constant regardless of the input, proving that these excess dimensions encode no mutual information and are entirely suppressed by the posterior collapse mechanism.

Figure 10: Architecture of the Raw-Space Co-Diffusion. Unlike GOLD’s unified latent manifold, this experiment performs independent diffusion processes (categorical and Gaussian) in their respective raw data spaces, fusing the noisy modalities solely through input-level concatenation.

Architecture	Seq Recovery ( $\uparrow$ )	SS Validity ( $\uparrow$ )	Clash Score ( $\downarrow$ )
Raw-Space Baseline	0.6036	0.8657	6.53
GOLD (Base)	0.6249	0.9040	4.51

Appendix

Table 11: Ablation study comparing the Unified Latent Manifold (GOLD) against the Raw-Space Co-Diffusion baseline on the GOLD Test Benchmark. All models are evaluated in the unguided (Base) setting using native outputs.

Model Variant	Seq Recovery ( $\uparrow$ )	SS Validity ( $\uparrow$ )	Clash Score ( $\downarrow$ )
GOLD (Base)	0.6249	0.9040	4.51
GOLD (Base w/ Input SS)	0.6253	0.9045	4.48
GOLD (SS-Guided)	0.6267	0.9343	4.32

Appendix

Table 12: Ablation study on the utilization of Secondary Structure (SS) information evaluated on the GOLD Test Benchmark. Applying the target SS merely as an input edge feature yields minimal gains, demonstrating that the dynamic gradient intervention (SS-Guided) is the fundamental driver of topological accuracy.

Method	Novelty	Success Rate ( $\uparrow$ )				Diversity
		2Å	5Å	8Å	10Å
PiFold	0.2858	0.0327	0.1763	0.3184	0.3752	0.1148
RDesign	0.3291	0.0468	0.2227	0.3853	0.4566	0.0788
gRNAde	0.3254	0.0356	0.1938	0.3519	0.4298	0.0842
RiboDiffusion	0.2989	0.0668	0.3742	0.5189	0.6102	0.1264
SOLD	0.2949	0.0585	0.3913	0.5569	0.6321	0.1121

Appendix

Table 13: Sequence novelty, structural success rate, and intra-target diversity on the GOLD Benchmark.

$\omega_{\mathrm{ss}}\backslash\omega_{\mathrm{clash}}$	$0$	$0.05$	$0.10$	$0.50$	$1.00$
$0$	0.625/0.904/4.51	0.636/0.901/3.11	0.638/0.903/2.76	0.635/0.906/2.28	0.626/0.894/2.77
$1$	0.627/0.934/4.32	0.637/0.932/3.06	0.638/0.929/2.67	0.633/0.928/2.31	0.627/0.927/2.74
$2$	0.626/0.936/4.43	0.634/0.934/3.08	0.636/0.931/2.69	0.632/0.930/2.27	0.621/0.931/2.81
$3$	0.627/0.938/4.38	0.635/0.936/3.10	0.637/0.932/2.72	0.630/0.933/2.32	0.624/0.932/2.78

Appendix

Table 14: Interaction between secondary-structure and clash guidance on the GOLD Benchmark. Each cell reports Sequence Recovery / SS Validity / Clash Score (

\uparrow/\uparrow/\downarrow

). The default configuration is highlighted in bold.

Guidance	Weight	$\mathbf{KL}_{\mathrm{path}}$	SS Validity $\uparrow$	Clash Score $\downarrow$	Seq Recovery $\uparrow$
SS	$0$	$0$	$0.904$	–	$0.625$
SS	$1$	$0.075$	$0.934$	–	$0.627$
SS	$2$	$0.541$	$0.936$	–	$0.626$
SS	$3$	$0.905$	$0.938$	–	$0.627$
Clash	$0$	$0$	–	$4.51$	$0.625$
Clash	$0.05$	$10$	–	$3.11$	$0.636$

Appendix

Table 15: Guidance sensitivity and reverse-process deviation under different guidance strengths.

Figure 11: Observation of topology and sequence intervention under Topological Guidance ( $\omega_{ss}$ ) for target 2K5Z_A . Left ( $\omega_{ss}=0$ ): Without guidance, the generative trajectory leaves the stem partially open, producing unviable base pairs (highlighted in red). Right ( $\omega_{ss}=1.0$ ): The guidance gradient effectively corrects the pairing network by shifting the local sequence probability toward valid Watson-Crick pairs (highlighted in cyan). This intervention successfully closes the stem with 100% validity, illustrating how the model resolves physical conflicts without simply relying on sequence memorization.

Figure 12: Ablation of spatial guidance intensity ( $\omega_{clash}$ ) on targets 5WNV_B and 6C63_A . The data demonstrates that while an appropriate weight ( $0.1$ ) resolves physical clashes and preserves sequence recovery, excessive penalization ( $1.0$ ) leads to generative degradation.

Figure 13: Comprehensive Comparison on Target 4KNQ_B . Baselines exhibit severe topological collapse, whereas GOLD successfully recovers the global fold.

Figure 14: Comprehensive Comparison on Target 6Q8V_A . GOLD demonstrates superior sequence-structure fidelity, achieving 100% SS validity and the lowest RMSD (4.4Å) compared to baselines.

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RIDER: 3D RNA Inverse Design with Reinforcement Learning-Guided Diffusion

Tianmeng Hu, Yongzheng Cui, Biao Luo, Ke Li

University of Exeter · Central South University

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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.

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