Uncertainty Estimation for Molecular Diffusion Models
Paul Seij, Christian A. Naesseth, Stephan Mandt, Metod Jazbec
Abstract
Diffusion models have seen wide adoption for 3D molecular generation, yet they offer no principled signal of when a generated molecule is likely to be of low quality. We propose a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. Building on a Laplace approximation of the denoising network, we measure the variability of the noise prediction across the generation trajectory. Empirically, we show that the resulting uncertainty score is informative of sample quality, exhibiting a negative correlation with established sample-level quality metrics. We further study how the proposed uncertainty score can be used to filter generated samples, improving model performance via test-time scaling.
AI Impact Assessments
(1 models)Scientific Impact Assessment
1. Core Contribution
The paper introduces a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. The approach fits a Laplace approximation to the denoising network's parameters, draws weight samples from this posterior, and measures the variance of noise predictions across the sampling trajectory. This variance is aggregated over timesteps, atoms, and feature dimensions to produce a scalar uncertainty score per generated molecule. The key claim is that this score negatively correlates with sample quality metrics (molecular stability, atom stability, validity) and can be used for test-time filtering to improve generation quality without retraining.
The contribution is essentially an adaptation of existing uncertainty estimation techniques for image diffusion models (Kou et al., 2024; Jazbec et al., 2025) to the molecular domain. The novelty is thus incremental — the methodological machinery (Laplace approximation, noise prediction variability) is borrowed directly from prior work. The paper's value lies primarily in being a "first application" to molecular diffusion models and in demonstrating that the approach works (at least on QM9).
2. Methodological Rigor
The experimental setup is reasonable: two models (EDM, GeoLDM) with official pretrained checkpoints, two datasets (QM9, GEOM-Drugs), and comparison against a natural baseline (diffusion NLL). The use of Spearman rank correlation to assess the relationship between uncertainty and quality metrics is appropriate.
However, several concerns arise:
3. Potential Impact
The practical motivation is sound: molecular generation pipelines would benefit from cheap quality filters before expensive downstream evaluations (docking, DFT, wet-lab). If the method worked reliably across molecular complexity scales, it could save significant computational and experimental resources.
However, the current impact is limited by:
4. Timeliness & Relevance
The paper addresses a timely topic at the intersection of two active research areas: uncertainty estimation for generative models and molecular generation. The test-time scaling angle is particularly timely given recent interest in inference-time compute scaling. The problem of quality filtering in molecular generation is genuinely important for drug discovery pipelines.
5. Strengths & Limitations
Strengths:
Limitations:
Overall Assessment
This is a competent workshop paper that identifies an important practical problem and provides a reasonable first attempt at solving it. The adaptation of Laplace-based uncertainty estimation from image diffusion to molecular diffusion is straightforward but useful as an initial exploration. The main weaknesses are the limited novelty, the failure to generalize beyond QM9, and the modest effect sizes. The Fisher ablation, while honest, somewhat undermines the Bayesian motivation. The paper opens a research direction but does not yet provide a robust solution.
Generated Jun 12, 2026
Comparison History (18)
While Paper 1 offers a timely contribution to molecular generation, Paper 2 demonstrates higher potential scientific impact due to its broad, model-agnostic applicability. By solving a fundamental theoretical issue in ensemble learning (the L1-simplex paradox), Paper 2 provides advancements that benefit any field utilizing ensemble methods. Its ability to simultaneously achieve massive compression, faster inference, and improved probability calibration offers widespread real-world utility and methodological rigor that transcends the domain-specific boundaries of Paper 1.
Paper 1 addresses a highly timely and broadly impactful question: understanding the mechanics of RL post-training for reasoning in LLMs. Given the explosive interest in reasoning models (e.g., OpenAI o1, DeepSeek-R1), mechanistic insights into how RL training works—identifying strategy selection and strategy improvement as core mechanisms—provides both theoretical understanding and practical guidance for scaling. This has broad implications across the entire LLM community. Paper 2 addresses a more niche problem (uncertainty in molecular diffusion models) with solid but more incremental contributions and a narrower audience.
Paper 2 has higher potential impact due to its broader relevance to graph ML theory and practice: truncated positional encodings are ubiquitous across domains (molecules, social, knowledge graphs), and clarifying their expressivity under realistic computational constraints addresses a foundational gap. Its contributions are both theoretical (separation results; limits vs 1-WL; analysis of k-harmonic distances) and practical (guidance to mix PEs), likely influencing future GNN design and benchmarks. Paper 1 is useful and timely for molecular diffusion reliability, but is more domain-specific and post-hoc, with narrower cross-field influence.
Paper 2 addresses a critical gap in a highly impactful field (molecular diffusion models for drug discovery) by introducing a novel uncertainty estimation method. This allows for improved sample filtering and test-time scaling, offering broad applicability across generative AI and computational chemistry. In contrast, Paper 1 presents a standard application of existing semantic segmentation techniques to a narrower planetary science task, and its negative result regarding GANs lacks the methodological innovation and broader multidisciplinary relevance seen in Paper 2.
Paper 1 addresses a critical bottleneck in AI-driven molecular generation (quality control and uncertainty), offering direct, high-impact applications in drug discovery and materials science. While Paper 2 provides valuable insights into LLM interpretability, its focus on a specific architectural variant (Block AttnRes) makes its immediate scientific impact more niche compared to the broad, interdisciplinary utility of reliable molecular diffusion models.
Paper 2 introduces a broadly applicable theoretical framework (simulatable processes) that relaxes independence assumptions and recovers VC-style guarantees for dependent, computationally bounded data sources. This is conceptually novel, timely for modern ML settings involving simulators and complex dependencies, and potentially impacts learning theory, online learning/regret analysis, conditional sampling, and computational complexity. Its claims suggest wide cross-field influence and foundational relevance. Paper 1 is useful and practical for molecular diffusion model reliability, but is more domain-specific and post-hoc, likely yielding narrower impact than a generalization of the PAC model.
Paper 1 offers a highly timely and widely applicable solution to a critical bottleneck in LLM deployment (KV caching for RAG and agents). By enabling Position-Independent Caching with minimal code changes in vLLM, it drastically improves throughput and latency for real-world AI workloads. While Paper 2 provides a valuable methodological advance for molecular diffusion in drug discovery, Paper 1's immediate relevance to the massive, fast-growing ecosystem of LLM inference gives it a significantly broader and more immediate potential impact across the AI community.
AuthorityBench addresses a fundamental and timely problem—how citation-based authority signals cause LLMs to hallucinate—with a large-scale, rigorously designed benchmark (220K prompts, factorial design, multiple domains). This has broad implications for AI safety, misinformation, and the deployment of LLMs in high-stakes domains like law and medicine. Paper 2, while technically sound, addresses a narrower problem (uncertainty estimation for molecular diffusion models) with more incremental contributions (post-hoc Laplace approximation for filtering). Paper 1's breadth of impact, novelty of the benchmark design, and relevance to the rapidly growing LLM deployment ecosystem give it higher potential impact.
Paper 2 is more likely to have higher impact due to broader applicability and timeliness: quantization for efficient deployment affects many time-series and sequential models across domains (edge/IoT, robotics, finance, healthcare). Its dynamical-systems framing for PTQ sensitivity is a novel, general metric that works a priori, decoupled from quantizer/bit-width choices, and can apply even to black-box/compiled networks—high practical value. The proposed mixed-precision PTQ without calibration data or second-order costs suggests strong real-world feasibility. Paper 1 is useful but narrower to molecular diffusion and post-hoc uncertainty filtering.
Paper 2 addresses a critical methodological gap in generative models for 3D molecular generation by introducing a principled uncertainty estimation method. This has profound implications for AI-driven drug discovery, allowing for better quality control and test-time scaling. While Paper 1 presents a valuable clinical application, Paper 2 offers higher methodological innovation and broader potential impact across the rapidly growing intersection of generative AI and computational chemistry.