Diffusion Model

The framework operates in two distinct phases. The forward process systematically corrupts a true 3D RNA structure by adding Gaussian noise to atomic coordinates until they become a random distribution. The reverse process trains a neural network, typically an equivariant architecture, to iteratively remove this noise. Starting from pure noise, the model applies learned denoising steps to generate a valid structure. This is fundamentally different from variational autoencoders because the latent space is a sequence of progressively noisier states rather than a compressed bottleneck.

A critical architectural constraint for molecular generation is SE(3) equivariance. The predicted structure must rotate and translate consistently with the input. If the input noise is rotated, the denoised output must rotate identically. Diffusion models for RNA achieve this using tensor field networks or IPA (Invariant Point Attention) modules, as seen in AlphaFold 3. This ensures the generated coordinates are physically meaningful regardless of the arbitrary reference frame, preventing the model from learning spurious coordinate-dependent artifacts.

The generative power of a diffusion model is controlled by conditioning signals. The denoising network receives the RNA sequence as a primary input, typically via a sequence embedding from a pre-trained RNA language model. Additional conditioning can include:

• Template structures from homologous sequences
• Chemical probing data like SHAPE reactivity profiles
• Distance restraints from cross-linking experiments This multi-modal conditioning steers the diffusion trajectory toward a specific target fold rather than a random RNA structure.

Unlike deterministic predictors, diffusion models are stochastic. Running the model multiple times on the same input yields an ensemble of structures. This enables self-consistency analysis: regions with low variance across the ensemble are highly reliable. AlphaFold 3 outputs a pLDDT (predicted Local Distance Difference Test) score per residue, which is a confidence metric trained to correlate with true structural accuracy. For RNA, low pLDDT regions often correspond to flexible loops or intrinsically disordered segments, guiding experimental validation priorities.

Modern diffusion models like AlphaFold 3 operate on all-atom representations, generating coordinates for every heavy atom rather than just the backbone. Crucially, they jointly model non-canonical interactions including:

• Metal ion coordination (e.g., Mg²⁺ in ribozymes)
• Small molecule ligands and modified nucleotides
• Protein-RNA interfaces in ribonucleoprotein complexes This holistic approach captures the chemical environment that stabilizes tertiary folds, moving beyond simplified coarse-grained representations.

The performance of diffusion models is directly tied to training data quality. Models are trained on the Protein Data Bank (PDB), which contains experimentally resolved RNA structures from X-ray crystallography and cryo-EM. To overcome the relative scarcity of RNA structures compared to proteins, techniques like self-distillation are employed: the model generates a large synthetic dataset of predicted structures, which is then filtered by confidence and used to retrain the model. This bootstrapping approach, pioneered in AlphaFold, significantly improves generalization to novel folds.

The fixed Markov chain that systematically corrupts data by adding Gaussian noise over T timesteps. For RNA structure prediction, this process starts from the ground truth 3D atomic coordinates and progressively adds noise until the structure becomes indistinguishable from random coordinates. The noise schedule—typically a cosine or linear variance schedule—controls how quickly information is destroyed. Key properties: the process is tractable (closed-form sampling at any timestep) and variance-preserving, ensuring the final distribution approximates an isotropic Gaussian.

The learned reverse Markov chain that iteratively removes noise to generate structured data. A neural network—typically a U-Net or SE(3)-equivariant architecture for 3D coordinates—is trained to predict the noise component at each timestep. During inference, the model starts from pure Gaussian noise and applies learned denoising steps to reconstruct a valid RNA 3D structure. The reverse process requires hundreds to thousands of iterative steps, though recent DDIM (Denoising Diffusion Implicit Models) samplers enable deterministic, accelerated generation with fewer steps.

The theoretical framework unifying diffusion models with score matching. Instead of learning to predict noise directly, the model learns the score function—the gradient of the log probability density with respect to the data. This score points toward regions of higher data density, guiding the denoising trajectory. The connection is formalized through stochastic differential equations (SDEs), where the forward process is a continuous-time diffusion and the reverse process solves the reverse-time SDE using the learned score. This framework enables flexible sampling with predictor-corrector methods like Langevin dynamics.

A critical architectural constraint ensuring that predicted RNA structures are physically consistent regardless of coordinate frame. SE(3) equivariant diffusion models guarantee that rotating or translating the input noise results in an identically transformed output structure. This is achieved through:

• Tensor field networks that process 3D coordinates using spherical harmonics
• Invariant point attention (IPA) as used in AlphaFold 3, which operates on local frames
• Equivariant message passing that updates coordinates and features while preserving geometric relationships Without equivariance, the model would waste capacity learning arbitrary coordinate transformations.

Methods for guiding the diffusion process toward desired structural properties. In RNA structure prediction, conditioning signals include:

• Sequence embeddings from RNA language models like RNA-FM or RiNALMo, providing evolutionary context
• Multiple sequence alignments (MSAs) that encode co-evolutionary coupling information
• Template structures from homologous RNAs, injected via cross-attention or feature concatenation
• Chemical probing data such as SHAPE reactivity, integrated as auxiliary features Classifier-free guidance, where the model is trained with and without conditioning, enables tunable conditioning strength during inference by interpolating between conditional and unconditional score estimates.