Structure-constrained Language Diffusion

• The paper integrates explicit structural constraints and language conditioning to ensure semantically grounded and controllable generation across diverse modalities.
• It introduces architectural innovations such as latent space structuring, encoder-decoder schemes, and cross-attention mechanisms for modality-specific design.
• Empirical evaluations reveal that SLDM improves output fidelity in molecule, text, and medical image generation through refined constraint enforcement and dual-phase diffusion.

A Structure-constrained Language-informed Diffusion Model (SLDM) is a generative modeling paradigm that explicitly integrates structural priors and language-derived conditioning into the diffusion-based generation process. SLDMs are devised to address challenges posed by the discrete, structured, or semantically rich nature of data (e.g., molecules, structured text, medical images), where standard diffusion models may fail to guarantee structural fidelity, controllability, or semantic grounding. By enforcing constraints derived from explicit structures, schemas, or natural language, SLDMs substantially improve the alignment between generated outputs and desired specifications across multiple modalities.

1. Architectural Foundations and Multi-Modal Design

SLDMs operate by augmenting standard diffusion model pipelines with structural supervision, language-based conditioning, or both, at multiple stages of the generation and denoising process. The key architectural elements typically include:

• Latent space structuring: A high-dimensional, continuous latent space is engineered for the data modality in question (e.g., SMILES embeddings for molecules, angle space for proteins, contour-augmented tensors for medical images).
• Encoder-decoder mechanisms: Raw data are mapped to latent representations via modality-specific encoders, followed by optional compression layers. A decoder reconstructs the structured data, typically using autoregressive or transformer-based architectures.
• Structural constraint modules: These enforce the preservation of salient structural properties, such as scaffold anchoring in molecules, syntax control in text, or topology in images. Guidance is injected either at the input layer, via cross-attention in the denoising backbone, or through auxiliary loss terms.
• Language-based or multi-modal conditioning: Pretrained language encoders or vision-LLMs (e.g., MolT5, CLIP-variants) map text or descriptive prompts to embedding spaces, which modulate the generative process through cross-attention, semantic guidance heads, or contrastive objectives.

The SLDM paradigm is realized with both plug-and-play and end-to-end learning procedures. Typical backbones include transformer U-Nets for sequence data (Chang et al., 2024), image restoration SDEs for medical imaging (Zhang et al., 28 Jan 2026), and latent diffusion or masked token diffusion models for text and structured data (Xiong et al., 6 Jul 2025, Khanal et al., 12 Jan 2026).

2. Formulation of Diffusion and Constraint Mechanisms

The diffusion process in SLDMs adheres to standard forward (corruption) and reverse (denoising) kernels, adapted for the latent space and modalities involved:

• Forward process: Latent variables (e.g., $z \in \mathbb{R}^{L \times d_z}$) are gradually noised with a prescribed schedule, typically an isotropic Gaussian or multivariate wrapped distribution for angular or continuous data.

$$q(z_t | z_{t-1}) = \mathcal{N}\left( z_t; \sqrt{1-\beta_t} z_{t-1}, \beta_t I \right)$$

• Reverse process: A neural denoiser predicts noise or data reconstructions, parameterizing the reverse kernel as:

$$p_\theta(z_{t-1} | z_t, e) = \mathcal{N}\left( z_{t-1}; \mu_\theta(z_t, t, e), \sigma_t^2 I \right)$$

with the mean $\mu_\theta$ computed from predicted noise $\epsilon_\theta$ (see (Chang et al., 2024, Zhang et al., 20 Aug 2025)).

• Structural constraints: Enforced through
  • Contrastive learning on latent embeddings (InfoNCE loss) for invariance to surface forms (e.g., SMILES enumeration) (Chang et al., 2024).
  • Auxiliary structure-specific loss terms (e.g., endpoint connectivity, overlap repulsion) in atomic direction space for proteins (Gao et al., 2023).
  • Cross-attention between latent states and text/image-derived structure priors (e.g., CTA-CLIP for medical images (Zhang et al., 28 Jan 2026); syntax sequences for language (Zhang et al., 1 Oct 2025)).
  • Rule-based or learned edit agents applying discrete, interpretable feedback to maintain adherence to formal schemas (Khanal et al., 12 Jan 2026).
• Guidance mechanisms:
  • Classifier-free or classifier-based guidance is utilized to interpolate between unconditional and conditioned generations, allowing controlled trade-off between structure, properties, and semantic alignment (Zhang et al., 20 Aug 2025, Chang et al., 2024).
  • Two-phase or cascaded generation: Early diffusion steps anchor structural features, later phases optimize properties or semantics (Zhang et al., 20 Aug 2025).

3. Training and Optimization Protocols

SLDMs are trained with composite objectives that ensure accurate reconstruction, effective structural regularization, and successful semantic alignment:

• Variational objectives: Noise-prediction or evidence lower bound (ELBO) losses for denoising, per standard DDPM or SDE models.
• Structural loss terms: Auxiliary losses are imposed to enforce invariants or alignment with gold-standard structure (e.g., $$\mathcal{L}_{\text{struct}} = \mathbb{E}[\| s_{t-1}^* - s_{\text{gt}} \|_2^2 ]$$ in vascular topology (Zhang et al., 28 Jan 2026); InfoNCE or cross-entropy for structural and syntactic targets (Chang et al., 2024, Zhang et al., 1 Oct 2025)).
• Contrastive learning: For modality alignment (e.g., image-text, scaffold-property), contrastive divergence or cross-modal MSE objectives are used (Chang et al., 2024, Zhang et al., 28 Jan 2026).
• RL-based or MARL optimization: In some settings, prompt optimization and structural compliance are driven by policy gradients using rewards defined over structure, content, and semantic metrics (Khanal et al., 12 Jan 2026).

Optimization strategies vary, with most approaches relying on Adam-type optimizers and lengthy multi-stage training involving both frozen and finetuned encoders/decoders. Some frameworks permit “plug-and-play” extension to new constraints or properties without complete retraining, supporting efficient adaptation (Zhang et al., 20 Aug 2025).

4. Applications Across Modalities

SLDMs have demonstrated state-of-the-art or highly competitive performance across diverse structured-generation tasks:

Domain	Constraint/Structure	Language Input	Notable Results	Source
Molecule generation	Molecular graph/scaffold	Natural language	Validity 94.1%, FCD=0.20 (ChEBI-20), outperforms AR	(Chang et al., 2024)
Multimodal molecule gen.	Scaffold & property	Text + property	Scaffold similarity ~60%, property up to +34%	(Zhang et al., 20 Aug 2025)
Structured text (JSON)	Schema (fields/format)	Natural language	Task success 0.79, high novelty/diversity	(Khanal et al., 12 Jan 2026)
Medical images	CTA topology/contours	Vascular description	SSIM=0.8050, best clinical/reader scores	(Zhang et al., 28 Jan 2026)
Protein inpainting	Backbone geometric links	Residue sequence	6–11 Å connectivity error, best designability	(Gao et al., 2023)
Personalized text	Syntax, stylistic weights	Style descriptor	Mauve=0.533, accuracy=0.964 (Yelp sentiment)	(Zhang et al., 1 Oct 2025)

In all settings, ablation studies confirm that structural constraint modules and language-based conditioning are essential for high-fidelity, controllable, and semantically-aligned generation.

5. Empirical Evaluations and Benchmarks

Extensive empirical evaluation is a hallmark of SLDM research, with task- and modality-specific benchmarks:

• Molecule generation: Validity, uniqueness, novelty, alignment (BLEU, Levenshtein, Tanimoto), Frechet ChemNet Distance. SLDM outperforms leading autoregressive and diffusion baselines across all key metrics (Chang et al., 2024, Zhang et al., 20 Aug 2025).
• Structured text/JSON: Structural adherence (validity, completeness, compliance), semantic fidelity (precision, recall, F1), hallucination rates, wall-time per generation. Methods such as Agents of Diffusion and S³ produce significant gains in schema compliance (up to 98%) and content fidelity (+48% F1), with reduced hallucination compared to AR-LLMs (Khanal et al., 12 Jan 2026, Xiong et al., 6 Jul 2025).
• Medical imaging: SNR, ISNR, PSNR, SSIM, radiologist scoring, vessel segmentation accuracy. SLDM achieves superior quantitative and clinical performance, preserving vessel topology and allowing clinician-controlled enhancement (Zhang et al., 28 Jan 2026).
• Proteins and language: Geometry metrics (connectivity error, overlap), designability (scTM), structural n-gram overlap, style/fluency/diversity measures. Consistent improvements are reported when structural constraints are enforced (Gao et al., 2023, Zhang et al., 1 Oct 2025).

Ablations confirm that each constraint mechanism is critical: removal of contrastive or structure-specific loss often collapses validity or structural precision to near zero.

6. Theoretical Insights and Future Directions

SLDM research corroborates several key theoretical and practical principles:

• Bidirectional and parallel attention: Diffusion-based models intrinsically enable full-context planning at each denoising step—yielding advantages over autoregressive (AR) methods, particularly for enforcing global structure (Xiong et al., 6 Jul 2025, Zhang et al., 1 Oct 2025).
• Subspace restriction through scaffolding: Injection of schema, topology, or scaffold constraints collapses the generative search space to legal outputs, reducing hallucinations and boosting content and structural fidelity (Xiong et al., 6 Jul 2025, Khanal et al., 12 Jan 2026).
• Plug-and-play modularity: SLDM frameworks that permit independent structure and property control support rapid adaptation to new semantic, structural, or multi-modal specification, with lightweight training (Zhang et al., 20 Aug 2025).
• RL-enhanced controllability: Multi-agent reinforcement learning enables structure-aware editing of DLMs without the need for retraining generator parameters (Khanal et al., 12 Jan 2026).

Ongoing challenges include inference speed (still slower than GANs/AR in many settings), scalability to nested or highly complex schemas, reduction of dependency on paired data, and extension beyond current modalities (e.g., to code, tabular data, non-contrast medical imaging). Anticipated directions involve single-step consistency models for real-time applications, richer multi-agent hierarchies, and broader schema/constraint expressivity.

7. Significance and Impact

SLDM establishes a general design pattern for high-fidelity, structured, and controllable generation in settings where structure, semantics, or explicit constraints are central. By integrating explicit structure modules, language-based guidance, and cross-modal encodings with diffusion architectures, SLDM methods have advanced the state-of-the-art in text-to-molecule, structured data, and medical image generation, while providing principled routes for further extension to new domains and multi-agent control (Chang et al., 2024, Zhang et al., 20 Aug 2025, Zhang et al., 28 Jan 2026, Zhang et al., 1 Oct 2025, Khanal et al., 12 Jan 2026).

For reference to core literature, see (Chang et al., 2024) for text-conditioned molecule generation, (Zhang et al., 20 Aug 2025) for cross-modality molecular control, (Zhang et al., 28 Jan 2026) for medical imaging, (Khanal et al., 12 Jan 2026) for multi-agent schema-constrained text, (Xiong et al., 6 Jul 2025) for schematic scaffolding in language diffusion, (Zhang et al., 1 Oct 2025) for syntax and style-controlled language, and (Gao et al., 2023) for geometric constraint in protein inpainting.