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This paper claims that letting diffusion models change the number of atoms in a crystal during generation—via placeholder 'mirage' atoms—improves the quality of generated crystals by up to a factor of 2.5 and yields an 8.2% S.U.N. rate, exc

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2026-08-03 21:35 UTC pith:JOZWUU2B

load-bearing objection Mirage infusion is a clean, well-tested trick for variable-size crystal diffusion; the headline S.U.N. comparison is undercut by unmatched training budgets and evaluation pipelines. the 3 major comments →

arxiv 2511.14426 v2 pith:JOZWUU2B submitted 2025-11-18 cs.LG cond-mat.mtrl-scics.AIphysics.comp-ph

MiAD: Mirage Atom Diffusion for De Novo Crystal Generation

Andrey Okhotin , Maksim Nakhodnov , Nikita Kazeev , Mikhail Lazarev , Andrey E Ustyuzhanin , Dmitry Vetrov This is my paper
classification cs.LG cond-mat.mtrl-scics.AIphysics.comp-ph
keywords crystal generationdiffusion modelsmirage atomsvariable atom countS.U.N.de novo materials discoveryequivariant diffusiondensity functional theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that forcing diffusion models to generate crystals with a fixed number of atoms is a severe restriction, and that lifting it improves generation quality by a large margin. The proposed technique, mirage infusion, pads every crystal to a fixed larger size with placeholder 'mirage' atoms of a special type; during the denoising trajectory the model decides which placeholders materialize into real atoms and which vanish. On the standard benchmark for crystal generation, the resulting model (MiAD) reaches an 8.2% S.U.N. rate—stable, unique, and novel crystals—exceeding previous approaches, and improves the underlying joint diffusion model by up to 2.5x. The authors also provide ablations showing that uniform initialization of mirage positions and loss masking for mirages are important design choices.

Core claim

The central claim is that variable-size generation can be achieved within a fixed-size diffusion framework by reinterpreting atom insertion and removal as type transitions. Adding a special atom type '0' (mirage) and infusing crystals to a uniform size Nm, the model learns to jointly denoise lattice, coordinates, and types; the fractional-coordinate loss is masked for mirage atoms, so the model is free to decide their positions while learning when a mirage should become real. During sampling, all crystals start at the same size and the model removes the remaining mirages at the end. The authors show this yields crystals with varying atom counts and a substantially better trade-off between st

What carries the argument

Mirage infusion: an expanded crystal representation where every sample has exactly Nm atoms, with type 0 denoting a placeholder. The mechanism is an extra state in the discrete atom-type diffusion process plus a masking of the coordinate-denoising loss for placeholder atoms; this lets the model treat 'does this atom exist' as a continuous decision inside a standard equivariant denoiser. The same network architecture as the base joint diffusion model is retained, isolating the effect of the infusion.

Load-bearing premise

The headline comparison assumes that the S.U.N. numbers for prior models are measured equivalently; if the longer training (8000 vs 1000 epochs) or the evaluation pipeline (pre-relaxation and DFT thresholds) rather than mirage infusion drives the improvement, the central claim weakens.

What would settle it

Train the same base joint diffusion model without mirage infusion for the same 8000 epochs and evaluate it with exactly the same pre-relaxation and DFT protocol; if its S.U.N. rate matches or exceeds 8.2%, the mirage-infusion explanation is refuted.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Fixed-size diffusion models for crystals are leaving performance on the table; allowing size changes during generation can multiply the S.U.N. rate by up to 2.5.
  • The technique transfers without modification to other joint diffusion models that share the same crystal representation and loss factorization.
  • MiAD produces S.U.N. crystals across a wide range of atom counts, indicating that the model learns to use the added flexibility rather than collapsing to a single size.
  • Design choices matter: uniform initialization of mirage atoms and masking of their coordinate loss are critical; alternatives (center initialization, no masking) markedly reduce quality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If mirage infusion works because it converts discrete size selection into a continuous type decision, the same trick could apply to other generative settings with variable cardinality—for example, populations of particles or point clouds—where a fixed-size latent is inconvenient.
  • The masking choice suggests a general principle: when placeholder tokens have no ground-truth position, the model should be allowed to place them freely rather than being trained toward an arbitrary coordinate.
  • Because mirage infusion increases the number of atoms the network must process, future work may need to combine it with size-adaptive architectures or hierarchical sampling to keep inference costs manageable.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes 'mirage infusion' for crystal diffusion models. A special atom type 0 ('mirage') is introduced, and every training crystal is padded to a fixed number of atoms Nm by adding mirage atoms with uniformly random fractional coordinates. The coordinate denoising loss is masked for mirage atoms, while the lattice and atom-type losses are applied to the expanded structure. At sampling, all crystals start from Nm atoms and the final crystal is obtained by removing atoms whose predicted type is 0. The resulting model MiAD (DiffCSP + mirage infusion) is evaluated on MP-20 against diffusion, flow, and two-stage baselines using the S.U.N. metric under DFT and MLIP stability estimates. The authors claim 8.2% DFT S.U.N., a relative improvement over DiffCSP of up to about 2.5x, and report ablations over Nm, atom-type loss weighting, and design choices for the mirage representation.

Significance. If the claimed improvements survive scrutiny, mirage infusion is a simple, architecture-agnostic mechanism for variable-size generation in crystal diffusion models, with clear potential for transfer to MatterGen, FlowMM, and similar joint diffusion/flow models. The paper is honest about several auxiliary metrics being saturated and focuses on S.U.N., which is a sensible primary metric for de novo discovery. Strengths include a clean formulation, a public code link, informative ablations over Nm and loss scaling, and a comparison against an alternative mirage formulation from the drug-design literature. The main weakness is that the headline comparison is confounded: baseline numbers are imported from earlier papers with different evaluation pipelines, MiAD is trained for 8000 epochs while the DiffCSP baseline used 1000, and key hyperparameters are selected using the same S.U.N. metric on which the final claim is made.

major comments (3)
  1. [Table 1; §6; Appendix C] The central x2.5 claim is not causally identified. DiffCSP's 3.3% S.U.N. is quoted from Miller et al. (2024), while MiAD is computed with the authors' CHGNet-prerelax + DFT pipeline. Appendix C states that MiAD was trained for 8000 epochs with the learning-rate scheduler removed, whereas the original DiffCSP baseline used 1000 epochs. No DiffCSP run at 8000 epochs under the identical relaxation/DFT protocol is reported. The observed 3.3→8.2 gain and the x2.5 attribution could therefore be due to additional compute or a different prerelaxation/DFT pipeline rather than mirage infusion. The authors should provide a matched DiffCSP baseline: same epochs, same scheduler setting, same CHGNet prerelaxation, same DFT settings, and the same S.U.N. computation.
  2. [Tables 3-4; §B.1-B.2] The hyperparameters Nm and the atom-type loss coefficient LA are selected by maximizing S.U.N. on the evaluation metric, and the same S.U.N. value is then reported as the final result. This is selection-on-the-metric: the reported 8.2% / 5.5% values are optimistically biased relative to a model chosen without peeking at S.U.N. A held-out evaluation split, a nested model-selection procedure, or at least a report of the selection trajectory is needed. Without this, the claimed optimality of Nm=25 and LA×1.0, and the size of the final advantage over DiffCSP, are not well grounded.
  3. [Tables 1-5; §6] No error bars, multiple seeds, or repeated sampling are reported for any S.U.N. estimate. Several decisive differences are small: in Table 3, eq-V2 S.U.N. values are 5.3, 5.5, 4.7, 4.6 for Nm=20,25,30,35, and in Table 4, 4.7, 5.5, 5.0 for LA×0.5, ×1.0, ×2.0. Since S.U.N. is a ratio of 10,000 generated crystals and the evaluation pipeline includes stochastic prerelaxation, the differences among the top configurations may be within sampling noise. The authors should report variance over at least a few seeds or bootstrap intervals, especially for the ablation tables that are used to justify the final model choice.
minor comments (5)
  1. [Algorithm 2] Algorithm 2 samples 'M_T ∼ q(M_T)' and 'Denoise M_{t-1} = q(M_{t-1}|M_t)'. The prior and the learned backward kernel should be p(M_T) and p_θ(M_{t-1}|M_t); q is used for the forward process elsewhere. Please correct the notation.
  2. [Figures 2-3] The same comparison appears as 'Figure 2' in the main text and 'Figure 3' in Appendix B.4, with slightly different y-axis ranges and metric definitions. The main text says 'see Figure 2' but the figure is reproduced in the appendix. Please consolidate or clearly label the two figures to avoid confusion about which curves correspond to eq-V2 vs CHGNet.
  3. [Appendix C] The sentence 'Additional experiments confirmed that this modification in the optimization procedure does not influence the quality of the default DiffCSP' is not supported by a table or figure. If the claim is used to argue that the scheduler removal is harmless, the evidence should be shown.
  4. [Appendix E, Table 6] The caption says 'All results follow the same mirage infusion configuration as for MP-20', but the text states that for Perov-5 and Carbon-24 the configuration uses Nm=N+5 rather than Nm=25. Please state the configuration explicitly in the caption.
  5. [Appendix F] The statement that crystals with 3,7,11,13,17 atoms 'appear more rarely than others because crystals with these atom counts are underrepresented in the training data' would be more convincing with a histogram of the training-set atom counts overlaid on Figure 4.

Circularity Check

0 steps flagged

No circular derivation: mirage infusion is an empirical augmentation evaluated with external metrics; confounds are experimental, not circular.

full rationale

MiAD is an empirical method paper, not a derivation from first principles. The proposed technique is defined constructively (extra atom type, expanded fixed-size domain, masked fractional-coordinate loss, reduction operator), and the headline numbers come from external stability pipelines (DFT, CHGNet, eq-V2) and StructureMatcher, not from the model's own training objective. The central ablation in Figure 3 compares MiAD with DiffCSP under the same architecture, giving the improvement claim independent content. No fitted constant is renamed as a prediction: hyperparameters Nm and LA are selected using S.U.N. itself (Appendix B, Tables 3-4), which makes the final 8.2% S.U.N. an in-sample selection result rather than a fully independent test, and the DiffCSP comparison is confounded by unequal training budgets (Appendix C, 8000 vs 1000 epochs, scheduler removed). These are experimental validity concerns, not circular reductions of a derivation. The only overlapping-author citation (WyFormer, Kazeev et al. 2025) is used as a baseline and is not load-bearing for the mirage-infusion argument.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 1 invented entities

The central claim rests on the DiffCSP diffusion framework, MP-20 as training/evaluation data, DFT/MLIP stability proxies, and several design choices specific to mirage infusion. The most consequential free choices are Nm, the LA loss weight, the training budget, and the prerelaxation protocol; all were selected or influenced by the same S.U.N. metric used in the headline result.

free parameters (4)
  • Nm (maximum atom count in expanded domain) = 25
    Selected from {20, 25, 30, 35} to maximize S.U.N. (eq-V2/CHGNet) in Table 3; controls how many mirage atoms the model must prune during sampling.
  • Loss coefficient for atom-type component (LA) = 1.0
    Chosen by ablation in Table 4; final loss priority (L-F-A) is 36-46-18, which the paper treats as optimal but was tuned on the same S.U.N. metric.
  • Training epochs = 8000
    MiAD peak S.U.N. is reached at 8000 epochs (Figure 3), versus 1000 epochs for the original DiffCSP; compute budget differs between models.
  • Prerelaxation steps for stability evaluation = 1500 (CHGNet) / 100 (eq-V2)
    Protocol choices in Section 5; different prerelaxation can change Ehull and S.U.N., and not all baselines use the same protocol.
axioms (6)
  • standard math Lattice, fractional-coordinate (wrapped normal), and atom-type (D3PM) diffusion objectives from DiffCSP are valid and equivariant.
    Used as the base model; MiAD inherits its correctness.
  • domain assumption MP-20 and the Materials Project convex hull adequately represent stable inorganic crystals.
    Training data and stability reference; biased toward known materials.
  • domain assumption Ehull from DFT (or CHGNet/eq-V2 proxies) is an appropriate stability proxy for S.U.N.
    Section 5 acknowledges DFT vs MLIP differences and uses thresholds Ehull<0 and <0.1 eV.
  • ad hoc to paper Mirage atoms do not need ground-truth coordinates; masking their coordinate loss yields a valid denoising target.
    Eq. (2) in Section 3; the paper assumes atoms that convert mirage-to-real can be sampled correctly despite never seeing clean positions for such atoms in training.
  • ad hoc to paper Uniform initialization of mirage coordinates is a reasonable and valid choice.
    Section 3 Discussion and Table 5; empirically chosen over center-of-mass, not derived.
  • domain assumption StructureMatcher with default parameters defines uniqueness and novelty.
    Section 5; follows baselines, but matching tolerances affect S.U.N.
invented entities (1)
  • Mirage atom (type 0) no independent evidence
    purpose: Placeholder atom that can become real or vanish during generation, allowing variable Natoms in a fixed-size diffusion model.
    Internal modeling construct; its existence is only evidenced through generation-quality metrics, not a direct falsifiable prediction.

pith-pipeline@v1.3.0-alltime-deepseek · 21516 in / 12981 out tokens · 118742 ms · 2026-08-03T21:35:48.019170+00:00 · methodology

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read the original abstract

In recent years, diffusion-based models have demonstrated exceptional performance in searching for simultaneously stable, unique, and novel (S.U.N.) crystalline materials. However, most of these models don't have the ability to change the number of atoms in the crystal during the generation process, which limits the variability of model sampling trajectories. In this paper, we demonstrate the severity of this restriction and introduce a simple yet powerful technique, mirage infusion, which enables diffusion models to change the state of the atoms that make up the crystal from existent to non-existent (mirage) and vice versa. We show that this technique improves model quality by up to x2.5 compared to the same model without this modification. The resulting model, Mirage Atom Diffusion (MiAD), is an equivariant joint diffusion model for de novo crystal generation that is capable of altering the number of atoms during the generation process. MiAD achieves an 8.2% S.U.N. rate on the MP-20 dataset, which substantially exceeds existing state-of-the-art approaches. Code: https://github.com/andrey-okhotin/miad.git

Figures

Figures reproduced from arXiv: 2511.14426 by Andrey E Ustyuzhanin, Andrey Okhotin, Dmitry Vetrov, Maksim Nakhodnov, Mikhail Lazarev, Nikita Kazeev.

Figure 1
Figure 1. Figure 1: Overview of the proposed mirage infusion technique. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of MiAD (DiffCSP with mirage infusion) and DiffCSP in terms of stabil￾ity, uniqueness, novelty, and S.U.N. Stability is estimated via eq-V2. Appendix B provides a detailed exposition of key design choices underlying the mirage infusion technique. Specifically, we illustrate that, within the proposed definition of the expanded domain, there exists flexibility in selecting Nm, the total number of … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of MiAD (DiffCSP with mirage infusion) in its final version and DiffCSP in [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Number of atoms in S.U.N. crystals generated by MiAD. We consider only S.U.N. crystals [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of models for de novo crystal generation in terms of numbers of S.U.N. [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

discussion (0)

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