Title: Straight-Line Diffusion Model for Efficient 3D Molecular Generation
Venue: NeurIPS 2025
Accepted: yes
Keywords: Molecule generation; Diffusion model
Abstract: Diffusion-based models have shown great promise in molecular generation but often require a large number of sampling steps to generate valid samples. In this paper, we introduce a novel Straight-Line Diffusion Model (SLDM) to tackle this problem, by formulating the diffusion process to follow a linear trajectory. The proposed process aligns well with the noise sensitivity characteristic of molecular structures and uniformly distributes reconstruction effort across the generative process, thus enhancing learning efficiency and efficacy. Consequently, SLDM achieves state-of-the-art performance on 3D molecule generation benchmarks, delivering a 100-fold improvement in sampling efficiency.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a novel diffusion process characterized by near-straight-line trajectories. To achieve this, the authors propose a new perturbing forward kernel designed to minimize the second-order truncation error in ODE discretization schemes (e.g., Euler’s method) for sampling. The primary application is 3D molecular generation, where the authors argue that the proposed diffusion process is particularly suitable due to the high noise sensitivity of molecular data. The model achieves faster sampling speeds without sacrificing performance.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\nThe paper proposes a reverse-engineering approach in which the authors first analyze the truncation error of first-order ODE solvers in sampling. They then design a diffusion process that cancels out higher-order terms, enabling the use of larger step sizes and accelerating the sampling process. To the best of my knowledge, this idea appears novel and interesting.\n\n**Weaknesses**\n\n- In terms of molecular generation, this paper heavily relies on the existing framework of UniGEM [1], adopting its model architecture and generation process for molecular atom types and coordinates. However, it remains unclear whether the proposed method offers substantial improvements, given that UniGEM [1] has already achieved strong performance. Notably, Table 1 lacks a direct comparison with UniGEM [1], making it difficult to assess the claimed advantages.  As a result, the paper appears to contribute only marginal novelty to the field of 3D molecular generation.\n\n- The paper does not provide sufficient justification for why a straight-line diffusion process is particularly suitable for molecular data. The explanation given between lines 41 and 45 is unconvincing. Intuitively, whether the diffusion follows a straight-line trajectory or not, small perturbations would still introduce noise and potentially generate invalid molecular conformations. In addition, one could argue that a straight-line diffusion process might struggle to adequately explore the whole molecular conformation or atom coordinate distributions, while standard stochastic perturbations could achieve better coverage, leading to more reliable and smoother data score estimation. Although the authors attempt to address this by introducing a small constant variance, they do not include an ablation study to show how varying this variance impacts model performance.\n\n- I remain skeptical about the novelty of molecules generated by the model trained under the small-variance straight-line diffusion process, particularly since the authors have not reported any novelty metrics to address this important aspect.\n\n- Furthermore, several key theoretical derivations lack clarity (see Questions).\n\nQUESTIONS:\n1) Line 43: It remains unclear why straight-line diffusion aligns well with molecular data (see Weaknesses)?\n\n2) Could the authors incorporate the novelty metric employed in the GeoBFN [2] framework? Specifically, how does the novelty of the generated molecules compare to the training set? It would also be helpful to discuss whether the low stochasticity in the straight-line constant-variance diffusion process increases the risk of the model memorizing training samples.\n\n3) Line 154: Could you clarify what is meant by a “more stable generative process” and why your proposed schedule leads to such stability? It is not immediately clear what Figure 2 is illustrating—is it showing the generative process or merely the forward noising process? If it is indeed the generative process, how is the same conformation generated across all three models? Based on the figure, it appears that GeoBFN achieves a stable conformation as early as step 4, whereas your method reaches a similar conformation only at the final step. This seems counterintuitive and appears to contradict the claim that your method accelerates the sampling of stable conformations.\n\n4) Table 1: Did you evaluate the results using multiple random seeds? It would be important to report the standard deviations as in the baselines to ensure a fair and meaningful comparison.\n\n5) How does the model's performance vary when using different constant sigma values? It would be helpful to understand the sensitivity of your method to this important parameter.\n\n6) Lines 145-147: It is unclear why the use of Langevin dynamics would make the trajectories to appear more linear or straight at the initial steps. Could you elaborate on the underlying mechanism or intuition behind this observation?\n\n7) Equation 7: It is unclear where the parameter $\\beta_t$ comes from? Although Appendix A.5 discusses it, the choice of $\\beta_t$ remains non-trivial and would benefit from further explanation. Moreover, in Algorithm 2, the purpose of the inner condition is not clearly stated. Could you elaborate on its role?\n\n8) It would be helpful to include a discussion comparing the training processes of UniGEM and the proposed framework. Specifically, why does the straight-line diffusion approach result in significantly longer training times than the standard diffusion method—10 days versus 7 days on QM9, and 16 days versus 6.5 days on GEOM-Drugs—despite both methods using the same architecture, learning rate, and optimizer? Intuitively, one might expect that using a simpler straight-line constant-variance diffusion would accelerate training as well. Clarifying this discrepancy would strengthen the experimental section.\n\nReferences\n\n[1] UniGEM: A Unified Approach to Generation and Property Prediction for Molecules. In ICLR25.\n\n[2] Unified Generative Modeling of 3D Molecules via Bayesian Flow Networks. In ICLR24.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-02"}

comments: SUMMARY:
The paper proposes a type of diffusion model specifically designed for 3D molecular generation. The core idea is to choose a schedule \mu and \sigma of the SDE to achieve a near straight-line backward process. This allows the model to produce high quality samples with 
a significantly smaller number of steps.

STRENGTHS AND WEAKNESSES:
**Strengths:**

1. The goal of the method is to generate molecular samples with a small number of steps. The technical motivation for that is natural and clear: To reduce the error of first order discretization, choose a schedule of the diffusion SDE so that the backward process is linear. The exposition revolves around this motivation and is clear and self-contained.

2. The experimental results shown in Table 1 and Figure 4 are impressive, demonstrating that the method achieves significant speed up over the baselines with better quality.

**Weaknesses:**

1. There are plenty of works focusing on accelerating diffusion generation for other domains such as image generation (e.g. [1]). In the experimental setup (Section 4.1) the authors only seem to compare to methods already used in molecular generation. I suspect directly adapting the progress in fast image generation to molecular generation can already give significant speed-up. More such experimental comparison is favorable.


*References:*
[1] Consistency Models, Song et al.

QUESTIONS:
1. In Appendix A.4, I don't quite understand the logic jumping from the toy example of delta distribution to a general data distribution. Is it just a loose analogy, without rigorous mathematical reasoning or intuition?

LIMITATIONS:
I do not have much to say about it.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-01

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a straight-line diffusion method (SLDM) for generating molecules in 3D. A unified framework is presented to understand truncation errors that lead to low-efficiency sampling across existing diffusion, flow matching, and Bayesian flow methods for molecular generation, framing them all as continuous-time ODEs. It is observed that large-magnitude second-order terms in the numerical approximation to the backward solution trajectory of the ODE necessitates small step sizes that limit efficiency. To mitigate this, SLDM is proposed to enforce a near-linear sampling trajectory that minimizes second derivative magnitudes and allows for larger step sizes and higher efficiency generation. Additional algorithmic components are introduced to improve sampling fidelity, including a Langevin dynamics term with time-annealing temperature control. Results are included and compared to baseline methods for unconditional and conditional generation with QM9, GeomDRUGs, and toy datasets.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The approach taken “[to] understand why existing methods suffer from low efficiency, we analyze the issue through the lens of truncation error in sampling” is well-posed \n2. Establishing a unified framework for assessing this over diffusion, flow matching, and BFNs is nice, framing them all as “as continuous-time Ordinary Differential Equations (ODEs)”\n3. The observation (line 31) that second-order terms can be large and connecting this why small step sizes are required to reduce truncation error (ie readout) is very useful. Proposing a solution to “strive for a linear sampling trajectory,\" i.e., to push the 2nd-order term toward 0 is also well-posed\n4. Introducing a linearly decaying $\\mu(t) = 1 - \\frac{t}{T}$ w/ small constant $\\sigma$ to guarantee a near-linear trajectory is really nice\n5. Strong results in Figure 1 (speedup w/ high stability) and Table 1 (generation quality metrics). In particular, it’s quite impressive to achieve rather high validity & stability while predicting bond types from coordinates, meaning that the geometries generated are quite good\n6. Introducing the Langevin component to mitigate observed initial deviations from linear sampling in the stochastic sampler is really nice\n7. Figure 2 demonstrating the slow diffusion, stable process, unfolding uniformly from the origin appears quite realistic and elegant (though see questions)\n\nWeaknesses:\n1. Predicting atom types based on coordinates instead of diffusing jointly. I see that UniGEM is referenced as having \"superior performance,\" but I don’t understand the chemical feasibility of generating 3D coordinates without knowing atom types, as the same set of atoms could have any number of reasonable geometries depending on what the atom types of each node are. Or, ie, the atom identities are typically thought to \\textit{determine} the geometry (and they do). So is the idea here to learn geometries of nodes that sort of implicitly contains atom-type information and purely from data, then fill in atom types post-hoc? This seems like it would limit generalization capacity, but I could be wrong. Please comment\n2. The baseline ($N_{atoms}$ classifier) for conditional generation is not super relevant – better would be to train a real classifier from, e.g., 2D graphs or 1D strings. Or, more realistically, to compare to other conditional or classifier-guided generation methods from the literature, particularly given that the conditioning mechanism here seems to be fairly simplistic, though it is barely formulated or discussed. More information on how the conditional generation is done would be nice, as this is an important setting\n3. Molecular stability is not included in GeomDRUGs, which leads one to assume it’s fairly low. This might be reasonable given it is challenging, but there are methods that can achieve strong performance (e.g., VoxMol). Please comment, strong results here would increase significance of the work\n4. Very slow training (Appendix E, line 822)\n\nQUESTIONS:\n1. Could you clarify why the SLDM formulation results in the deviation from linear sampling at early steps, ultimately correcting to linear? \n2. After line 154 (and in Figure 2), it is said that “the process unfolds uniformly from the origin, preserving the relative spatial relationships of atomic coordinates in intermediate states.” How is this so? I also don’t quite understand how the process unfolds from the origin, is this in the forward or reverse process? And is this a part of the implementation? Please clarify. One could imagine with a set of atom types initialized from the origin, there are many ways to unfold the process; if chemical/spatial relationships are preserved, you might observe that the final structure is essentially determined in early time steps. Is this what you see and is this beneficial? Or, do you observe that the initial unfolding involves some structure (atom-type) rearrangements, ie, that the early states have a degree of flexibility or stochasticity before the final molecule is largely determined? One might imagine this would be beneficial to prevent forms of memorizing from the initial origin (ie v high noise state), which seems to be what plagues other methods. Is this what's taken care of by time-annealing temperature schedule for the Langevin in (9)?\n3. Is Figure 2 showing forward or reverse processes? Sort of confusing matching with the main text description in 155–162 and noise scheduling in Figure 3\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
This paper proposes Straight-Line Diffusion Models (SLDM) for 3D molecular generation. The authors design a special noise schedule for training diffusion models, which then can be used to generate novel molecules with time-annealing sampling. Experiments shows SLDM has noticeable advantage in generation speed and quality compared with other models.

STRENGTHS AND WEAKNESSES:
Strengths:
1. Research on fast molecule generation is important for the AI for Science area as the generation speed of existing methods is still unsatisfactory.
2. The paper is clearly written and easy to follow.
3. SDLM indeed shows strong performance when sampling with only 50 steps. It seems very promising. Overall, SDLM could be a valuable contribution to the molecule generation community.

Weaknesses:
1. Recently, fast sampling from diffusion models usually relies on ODE solvers instead of directly sampling from the SDE trajectory. Could the authors add ODE results for the experiments in Section 4? I wonder if using ODE solvers can get even faster generative model.
2. It would be better if the authors can provide some qualitative examples of the generated molecules to help readers intuitively understand the generation quality.

QUESTIONS:
See Weaknesses.

LIMITATIONS:
N/A
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03