Summary
DiffCSP is a novel diffusion model for predicting crystal structures conditioned on the crystal's atom composition; it can also be extended to an initio crystal generation (sampling both atom composition and positions). Crystal modeling is challenging due to its periodic symmetry. DiffCSP proposes to solve periodicity constraints by diffusing on fractional coordinates and jointly generating the lattice and atom coordinates. Fractional coordinate diffusion is achieved with torsional diffusion that constraints each intermediate state to stay within a bounding box, i.e. a fixed unit cell. When compared with existing methods, DiffCSP is state-of-the-art across DFT and ML-based methods in predicting the crystal structures on three datasets -- Perov-5, Carbon-24, and MP-20 -- while requiring less computation. It is also state-of-the-art on ab initio generation for the same datasets.
Strengths
- Using fractional coordinates to handle periodicity is supported by several prior studies on crystal structures. It is encouraging to see DiffCSP explore this representation in diffusion models. The authors do a in-depth comparison with CDVAE [1] which alternatively explored a multi-graph construction for handling periodicity.
- DiffCSP studies joint diffusion over all three components of crystal structures: atom types, lattice matrix, and coordinates. The comparisons and benchmarks will be useful to the broader community.
- The denoising model, a modified EGNN, to achieve the periodic E(3) symmetry has architectural choices that are well motivated. Each component is ablated to demonstrate their individual importances.
- DiffCSP achieves state-of-the-art in crystal structure prediction and ab initio crystal generation.
[1] https://arxiv.org/abs/2110.06197
[2] https://arxiv.org/pdf/2102.09844.pdf
Weaknesses
- The authors claim DiffCSP is the first generative model for crystal structure prediction (CSP). I am curious to know why a generative viewpoint of CSP is beneficial. Discussion of why diffusion is important for this task would help, i.e. a discussion about uncertainty in the problem and how it manifests.
- The benefit of diffusing over the lattice could use more explanation. The ablation seems to show there is marginal benefit of diffusing the lattice. It is also not clear to me if gaussian diffusion is the right choice for the lattice vectors which can also be parameterized with 6 unique, rotation invariant parameters using the Niggli algorithm [1].
- DiffCSP is E(3) and periodicity equivaraint however CDVAE is SE(3) and periodicity equivariant. Perhaps I missed it but I do not see discussion on the subtley between E(3) and SE(3). It would be important to note this difference and include it in the discussion.
- A major consideration when performing joint diffusion is the noise schedules used for each diffusion process. A discussion of whether this was important practically would be helpful in the main text.
[1] https://pubmed.ncbi.nlm.nih.gov/14691322/
Questions
Concrete questions pertaining to my weaknesses:
- If there's a single right answer of the structure for a given atom composition then is it right to generate many possible structures? The author evaluate DiffCSP and other generative models by matching the samples to the ground truth structure to pick the best sample. But how would one select the best sample if the ground truth was not available?
- What is the rationale behind gaussian diffusion for the lattice parameters? Are magnitudes of the lattice bounded? If it is unbounded then it seems strange to use gaussian diffusion.
- Why is DiffCSP chosen to be E(3) equivariant but not SE(3) equivariant like in CDVAE? Is this a limitation?
- Was the noising schedule of the atom types, lattice, and coordinates important? Did it make a practical difference?
Other questions:
- Could Table 1 include mean and standard deviation for RMSE? If it doesn't fit then in the appendix would be fine. It would be helpful to know the spread of the metrics when multiple samples are used.
- How diverse are the crystals when multiple samples are drawn?
Typoes/suggestions:
- Line 33. Reference 11 does protein structure generation, not prediction.
- It would be helpful to include mean and standard deviation for RMSE in Table 1. If it doesn't fit then in the appendix would be fine. It would be helpful to know the spread of the metrics when multiple samples are used.
- It is odd to frame diffusion on the fractional coordinates as a DDPM when it is really a VE-SDE following the SDE formulation. I believe it will cause less confusion if some clarification is given to the original source of the torsional diffusion formulation as Riemannian score-matching [1].
[1] https://arxiv.org/abs/2202.02763
Rating
8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Limitations
- A potential limitation is SE(3) vs. E(3) equivariance. The authors do not discuss this. I have mentioned this already in the questions.
- The authors do not discuss choice of diffusion hyperarameters which I believe would have lots of practical use for researchers who would build on top of this work.