Clari: Generative Model for Organic CSP

• Clari is a generative model for organic crystal structure prediction that uses flow matching to generate non-redundant unit cells, reducing computation from minutes to seconds.
• It replaces expensive triangle layers with pair-bias attention, lowering memory and compute costs from cubic to quadratic scaling for larger crystals.
• By using explicit-hydrogen all-atom outputs from atom/bond graphs, Clari enables direct energy ranking without additional post-processing, expanding chemical applicability.

Searching arXiv for the primary paper and closely related work. Searching arXiv for "Clari organic crystal structure prediction flow matching". Clari is a generative model for organic crystal structure prediction (CSP) based on flow matching. It is designed to generate redundancy-free unit cells and to replace triangle layers with pure pair-bias attention, with the stated aim of reducing CSP from minutes per molecule to seconds while surpassing OXtal’s solve rate on OXtal’s test sets (Lo et al., 2 Jun 2026). Clari requires only atom types and bonds as input and does not need an RDKit-sanitizable input molecule, which expands its applicability to challenging chemistries such as fullerenes, metal complexes, and atom clusters. Because it models explicit hydrogens, it supports inference-time scaling via direct energy ranking, without any decoration or relaxation step (Lo et al., 2 Jun 2026).

1. Problem setting and design objective

Organic crystal structure prediction is presented as a requirement for computational modelling of organic solids, but traditionally costs several CPU-years per molecule. Generative models such as OXtal reduce this cost by sampling stable organic crystal structures directly, but OXtal forgoes explicit lattice parametrization in favour of modelling large crops of the bulk material with expensive triangle layers, which can incur a computational cost of minutes per molecule (Lo et al., 2 Jun 2026).

Clari addresses this regime by generating exactly one unit cell at a time, jointly modelling all the atoms and the three lattice vectors as “points.” This removes the redundancy associated with modelling multiple symmetry-related molecular copies in large bulk crops. The stated consequence is a reduction in computational cost together with broader applicability: the model uses only an atom/bond graph, does not require an initial 3D conformer, and does not require RDKit sanitization. The inclusion of explicit hydrogens is central to downstream ranking and simulation readiness (Lo et al., 2 Jun 2026).

A plausible implication is that Clari is positioned not merely as a faster variant of prior generative CSP systems, but as a reformulation of the representation itself: the unit cell, rather than a bulk crop, is the primary generative object.

2. Representation and architecture

Clari uses a Diffusion Transformer (DiT) backbone with modern advances including gated attention, SwiGLU activations, QKNorm, and a pair-bias mechanism in self-attention. The three lattice vectors are represented as virtual “lattice tokens,” so that lattice geometry and atomic geometry are mixed throughout the transformer layers. Input features include atom types, bonds, atomic charges/degrees/radii, adjacency, geographic and topological distances, fractional coordinates, and self-conditioning estimates (Lo et al., 2 Jun 2026).

The architectural change emphasized in the paper is the replacement of triangle layers with pair-bias attention. In the provided summary, this is described as reducing memory and compute cost from cubic to quadratic scaling, enabling training and inference with much larger models and larger crystals. No triangle message passing or 3D geometric equivariance is imposed; instead, the model is described as learning such symmetries via data and augmentation (Lo et al., 2 Jun 2026).

The following comparison summarizes the representation-level distinctions reported for Clari and OXtal.

Aspect	Clari	OXtal
Representation	Redundancy-free unit cell, explicit hydrogens	Bulk crop, heavy-atom only
Architecture	DiT backbone, pair-bias attention, no triangle layers	Triangle layers, bulk crops
Input requirements	Atom/bond graph (no sanitizable molecule or 3D conformer needed)	RDKit-sanitizable, relaxed 3D conformer

These design choices are presented as the main enablers of Clari’s speed and chemical scope (Lo et al., 2 Jun 2026).

3. Flow matching formulation and training design

Clari uses flow matching to generate the continuous transformation between a tractable source distribution and the empirical data distribution. The reported objective is

$$L_{\mathrm{FM}} = \mathbb{E}_{t,\, z_0,\, z_1}\left[\,\bigl\| v_\theta(z_t, t) - (z_1 - z_0) \bigr\|^2\right]$$

where $z_0$ is initialized from the source distribution, $z_1$ is the true data, $z_t = (1-t)z_0 + t z_1$, and $v_\theta$ predicts the velocity field. The training loss splits the lattice and coordinate terms (Lo et al., 2 Jun 2026).

The paper further reports auxiliary losses intended to improve physical validity and lattice accuracy. These include a relative lattice-volume loss,

$$L_{\mathrm{vol}} = \left|\frac{|\det \hat{L}_1|}{|\det L_1|} - 1\right|$$

and a pairwise periodic distance loss,

$$L_{\mathrm{pair}} = \sum_{(i, j) \in \Lambda} \bigl| \hat{d}_{ij} - d_{ij} \bigr| + 5 \cdot \max(0, \alpha_{ij} - \hat{d}_{ij})$$

combined with the base flow-matching loss in the final objective (Lo et al., 2 Jun 2026).

Several ablations are highlighted. Treating the lattice as separate tokens rather than pooling atom features, adding auxiliary losses, and incorporating self-conditioning are all reported to lead to strong improvements in quality and reconstruction metrics. The timestep distribution is described as a critical hyperparameter: uniform or “mid-focused” schedules such as logit-normal, ramp, or beta can improve performance, while emphasizing very late times is worse for crystals. This suggests, as the summary explicitly notes, that global lattice and packing geometry forms at mid-timesteps rather than only during late-stage local refinement. For the source prior, a standard Gaussian for lattice vectors leads to degenerate or unphysical lattices, whereas a data-driven prior based on density, angles, and length marginals yields much better performance and physical plausibility (Lo et al., 2 Jun 2026).

4. Alignment, inference, and energy ranking

Before flow-matching interpolation, the target structure is approximately aligned to $z_0$ using brute-force signed permutation of lattice vectors, atom permutation using isomorphisms and the Hungarian algorithm, and weighted pose alignment via Kabsch. This alignment procedure is reported to improve the learning of proper symmetries and invariances (Lo et al., 2 Jun 2026).

At inference time, explicit hydrogens enable direct ranking of generated candidates using surrogate crystal energy models such as UMA. The reported best-of-$N$ procedure is to generate $n_s$ samples, compute their energies, and report the best $z_0$0 as solved according to the structural criteria used in evaluation. Because no hydrogen decoration or relaxation is required, energy ranking is described as a direct extension of generation rather than a separate post-processing pipeline (Lo et al., 2 Jun 2026).

This inference design is central to the model’s claimed scalability. The paper states that Clari can predict crystals in seconds rather than minutes or hours, and that this makes large-scale virtual screening of organic solids practical. It also states that the model can process crystals with up to 512 atoms in the unit cell (Lo et al., 2 Jun 2026).

5. Benchmarks, metrics, and empirical performance

On OXtal’s test sets, Clari is reported to surpass OXtal’s solve rate while obtaining a speedup of $z_0$1–$z_0$2. When generating 150 crystals and selecting the top-30 by energy, it further improves solve rate while maintaining a speedup of $z_0$3–$z_0$4. The details also report that generation plus energy ranking for 150 candidates per target takes approximately 6 seconds per molecule on an H100 GPU (Lo et al., 2 Jun 2026).

The evaluation criteria summarized for the paper include solve rate $z_0$5, clash rate, PoseBusters pass rate, relative volume error, and EMD PDD. Solve rate is defined as the fraction of targets with at least one generated candidate matching the experimental structure by COMPACK, with “8/15 heavy atom RMSD < 2Å, no inter-body clash” given as the matching criterion (Lo et al., 2 Jun 2026).

The summary table in the source material reports the following direct comparison.

Metric	Clari	OXtal
Speed (per molecule)	2–6 s (with ranking)	30–180 s
Solve rate (Sol@30, OXtal test)	Up to 0.772 (rigid), 0.346 (flex), 0.484 (Teach.)	0.300 (rigid), 0.220 (flex)
Energy ranking readiness	Yes, all-atom	Needs hydrogens, decoration, or relaxation

The paper also introduces the CSD Teaching Subset as a new test split of diverse and complex molecules for future benchmarking. This subset is described as containing approximately 773 test crystals, including fullerenes, boranes, organometallics, VSEPR types, and flexible rings. The reported solve rate on this subset is $z_0$6 for Clari-L (Lo et al., 2 Jun 2026).

6. Scope, chemical applicability, and disambiguation

A major stated feature of Clari is that it does not require RDKit-sanitizable input molecules. The paper explicitly connects this to applicability on challenging chemistries such as fullerenes, metal complexes, and atom clusters. Because the outputs are all-atom structures with explicit hydrogens, the system is presented as suitable for downstream energy models and large-scale virtual screening in domains such as optoelectronics and pharmaceuticals (Lo et al., 2 Jun 2026).

The name “Clari” should be distinguished from several unrelated systems in other research areas. “ClariCodec” is a neural speech codec operating at 300 bps that optimizes intelligibility with reinforcement learning (Wang et al., 19 May 2026). “CLARI” is a miniature modular origami passive shape-morphing robot (Kabutz et al., 2023), and “mCLARI” is a smaller body compliant quadrupedal microrobot with omnidirectional laterally confined locomotion (Kabutz et al., 2023). “CLARIFY” refers to contrastive preference reinforcement learning for ambiguous preference queries (Mu et al., 31 May 2025), while “ClarifyCoder” is a clarification-aware fine-tuning framework for programmatic problem solving (Wu et al., 23 Apr 2025).

Within organic CSP, however, Clari denotes the unit-cell flow matching model introduced in 2026. Its contribution is defined by four linked elements: redundancy-free unit-cell generation, pair-bias attention in place of triangle layers, explicit-hydrogen all-atom outputs, and inference-time energy ranking without decoration or relaxation. Taken together, these contributions are presented as enabling CSP within seconds and making large-scale virtual screening of organic solids practical (Lo et al., 2 Jun 2026).