Title: Dynamic Diffusion Schrödinger Bridge in Astrophysical Observational Inversions
Venue: NeurIPS 2025
Accepted: yes
Keywords: Diffusion Schrödinger bridge

Astrophysics

ML4Science
Abstract: We study Diffusion Schrödinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the Astro-DSB model, a variant of DSB with the pairwise domain assumption tailored for astrophysical dynamics. By investigating its learning process and prediction performance in both physically simulated data and in real observations (the Taurus B213 data), we present two main takeaways. First, from the astrophysical perspective, our proposed paired DSB method improves interpretability, learning efficiency, and prediction performance over conventional astrostatistical and other machine learning methods. Second, from the generative modeling perspective, probabilistic generative modeling reveals improvements over discriminative pixel-to-pixel modeling in Out-Of-Distribution (OOD) testing cases of physical simulations with unseen initial conditions and different dominant physical processes. Our study expands research into diffusion models beyond the traditional visual synthesis application and provides evidence of the models' learning abilities beyond pure data statistics, paving a path for future physics-aware generative models which can align dynamics between machine learning and real (astro)physical systems.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this paper, the authors propose to use a Bridge Matching procedure in order to astrostatistical inverse problems within iant Molecular Clouds. Their method is similar to I2SB [1]. The authors introduce a few key changes however which improve the methods, especially on OOD tasks. More precisely, they assume a modelling noise which is Gaussian and also further condition the model based on the clean observation $y$ similarly to [2]. Finally, as the data in astrostatistical setting is extremely large, they proceed using patch based training and an aggregation method. They conduct their evaluation on two key physical processes from magnetohydrodynamics simulations. They show improvements over conditional diffusion model baselines especially in OOD settings. \n\n[1] I^2SB: Image-to-Image Schrödinger Bridge (2023) -- Liu et al. \n\n[2] Augmented Bridge Matching (2023) -- De Bortoli et al.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n\n* The use of I2SB techniques for astrostatistical problem is new. \n\n* The results regarding the differences with conditional diffusion models are quite compelling. \n\nWeaknesses:\n\n* There seems to be some confusion around methodological and technical terms (see below)\n\n* (Minor) It is not clear to me what is the significance of those results in the astrostatistical community as I am not an expert on the topic.\n\nQUESTIONS:\nL.8 “our proposed paired DSB method” > We would like to take the opportunity to clarify that “paired DSB” is non-sensical as DSB and any Schrodinger Bridge and Optimal Transport (OT) based method must work on unpaired data as one of the goal of OT is to discover said pairing. We are aware of some confusion in the literature but we feel like this misunderstanding should be properly addressed.\n\nL.28 “we argue that the true power of this reformulation lies in the fact that it allows for diffusion models to capture the underlying data dynamics” > There are other benefits of OT compared to diffusion models especially since they work in unpaired settings as highlighted above.\n\nl.167  > I2SB is not a special case of the Schrodinger Bridge problem. \n\nL.174 > In M1, compared to I2SB the authors introduce another noise variable in $y_1 - \\varepsilon$. Does this $\\varepsilon$ correspond to the one introduced in (1), i.e., when specifying the perturbation model. It seems to be the case reading l.178. How realistic is this assumption? \n\nL.183 > The proposed method in M2 has already been proposed in the literature in [1]. The only difference between [1] and the proposed model is that [1] would take $y - \\varepsilon$ as an input while the current model takes $y$ as an input. \n\nL.189  “framework and helps simultaneously obtain lower loss values with a faster convergence speed” > It is unclear to me if the claim of lower loss value is grounded or not as a model that takes $y$ as a conditioning will have more parameters than a model that doesn’t. I guess, the main question is: “Is the improvement in performance observed by the authors only due to the increased number of parameters or is it due to the modeling choices?” My guess is that the modeling choices matter however, I do not think that the current experiments are enough to support such a claim. \n\nL.202 > I think it would be very interesting to describe in more details the aggregation strategy of AstroDSB.\n\nL.214 > I am by no means an expert in astrophysics and therefore will provide comments based on a machine learning point of view here. However, it seems that 5707 training samples in the molecular density casse and 19100 training samples in the magnetic field strength case is way less than the size of classical datasets used in machine learning. I have a few questions there: 1) is the size of the training dataset considering the patch-based augmentation? 2) since the dataset is quite small, are there safeguards in place to show that the model does not memorize the example ground-truths?\n\nL.204 > While describing the astrophysical data, even though the authors give the size of the patch it would be interesting to also give the size of the molecular density and the magnetic fied strength, i.e., how may patches do I need to reconstruct the data?\n\nL.267 > It seems that the main method of evaluation in this work is to report the mean and standard deviations of the relative errors. The authors write an interesting paragraph about the limitation of the Mean Error (ME). Is it a novel observation or is it well-known in the literature?\n\nL.274 > While investigating the implementation details it seems that the method used by the authors rely on quite outdated methods. Notably using a time discretization of 1000 steps. I would like to encourage the authors to investigate recent works such as [2,3] to improve their results.\n\nFigure 3 (b) is extremely hard to parse.\n\n[1] Augmented Bridge Matching (2023) – De Bortoli et al. \n\n[2] Simpler Diffusion (SiD2): 1.5 FID on ImageNet512 with pixel-space diffusion (2024) – Hoogeboom et al. \n\n[3] Simple ReFlow: Improved Techniques for Fast Flow Models (2024) – Kim et al.\n\nLIMITATIONS:\nThe authors have explicitly addressed the limitations of their work in the conclusion.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Astro-DSB, a specialized Diffusion Schrödinger Bridge model for astrophysical inverse prediction tasks within Giant Molecular Clouds (GMCs). The authors adapt the I2SB framework with three modifications: (M0) pairwise marginal distribution matching, (M1) noise perturbation alignment with observational uncertainties, and (M2) observable enhancement throughout the diffusion trajectory. The method is evaluated on both synthetic magnetohydrodynamics (MHD) simulations and real observational data from Taurus B213, demonstrating improved performance over conventional astrostatistical methods and other ML approaches in both in-distribution (ID) and out-of-distribution (OOD) settings.\n\nSTRENGTHS AND WEAKNESSES:\npros\n1.The application of diffusion bridge models to astrophysical inverse problems represents a meaningful extension beyond traditional computer vision tasks, addressing scientifically important problems in star formation research.\n\n2. Unlike heuristic OOD definitions in vision tasks, this work provides principled OOD evaluation through variations in initial physical conditions and dominant physical processes, making the generalization assessment more scientifically grounded.\n\n3. The evaluation on real observational data from Taurus B213 demonstrates practical applicability beyond synthetic simulations, which is crucial for scientific applications.\n\n4.The reported 75% reduction in training time compared to conditional DDPMs while achieving superior performance is practically significant.\n\ncon s:\n1. The core technical contributions are relatively incremental modifications to existing I2SB framework. The three proposed modifications (M0, M1, M2) are straightforward adaptations rather than fundamental algorithmic innovations.\n\n2.The paper lacks theoretical analysis of why DSB should be particularly well-suited for astrophysical inverse problems compared to other generative approaches. The connection between the physical dynamics of GMCs and the SDE formulation is not rigorously established.\n\n3.The synthetic data comes from only two MHD codes (ENZO and ORION2), potentially limiting the generalizability of conclusions about OOD performance.\n\nQUESTIONS:\n1. How does the learned diffusion trajectory relate to the actual physical evolution of GMCs? The paper claims to capture \"dynamic evolution processes\" but doesn't establish this connection rigorously.\n\n2.The choice of λ = 0.1 for the observational noise appears arbitrary. How sensitive are the results to this parameter, and how should it be chosen for different observational scenarios?\n\n3. How does the method scale with the number of physical quantities to predict? Would the pairwise matching assumption (M0) become limiting for multi-output scenarios?\n\n4.The comparison with conditional DDPMs uses the same training epochs (100 vs 400), but it's unclear if this represents convergence for both methods. Could the DDPM performance improve with longer training?\n\n5.What specific aspects of the DSB formulation enable better OOD generalization compared to discriminative approaches? The explanation remains largely empirical.\n\nLIMITATIONS:\nThe approach is limited to paired training data, which may not always be available in real observational scenarios. please also refer to the cons and questions. thank you.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-19"}

comments: SUMMARY:
This paper applies Diffusion Schrödinger Bridge (DSB) models to astrophysical systems, focusing on Giant Molecular Clouds (GMC).

STRENGTHS AND WEAKNESSES:
- The methodology is technically reasonable and follows established frameworks for DSB-based modeling.

- However, the contribution appears quite incremental. The training procedure closely mirrors existing approaches such as I2SB and Bridge-TTS, and the inference relies on a standard aggregation technique. I do not see a clear methodological innovation that sets this work apart from prior DSB literature.

- Additionally, I believe the analysis is weak. While the results include robustness and generalization of the proposed method, there is no discussions or insights into why the proposed method performs better than baselines, or what aspects of the astrophysical context might benefit specifically from this approach. Additionally, I don't see the clear improvements compared to cDDPM,

- The explanation of the comparisons are missing, both in the main text and appendix.  Especially, I do not see how cDDPM is implemented.

QUESTIONS:
- Could the authors clarify how the cDDPMs were implemented? Was the prior simply replaced with a Gaussian, or were other modifications made?

- In Equation (5), it seems there is a typo: the RHS should likely use $x_1$ rather than $x_t$.

- In Equation (6), the loss term should be written as a squared norm.

LIMITATIONS:
Please refer to the points above on the lack of methodological novelty and limited depth of analysis.
TITLE: Official Review
CLARITY: 2
IMPACT: 1
ORIGINALITY: 1
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new method called Astro-DSB with a pairwise domain assumption for solving the problem of observational inverse prediction in giant molecular clouds related to star formation. Through physical simulations and real Taurus B213 observations, it shows the method enhances interpretability, learning efficiency, and prediction performance over traditional astrostatistical and machine learning approaches.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nOriginality: It innovatively adapts DSB models to astrophysical dynamics, introducing the Astro-DSB framework with pairwise domain assumptions—a novel extension beyond traditional visual synthesis applications. It also introduces noise-aligned conditioning and step-wise observation injection.\n\nQuality: The research is rigorously supported by comprehensive experiments on both simulated magnetohydrodynamic data and real Taurus B213 observations. Quantitative results highlight Astro-DSB’s superior performance (e.g., reduced relative error μ=0.51±2E-4 in OOD density prediction) and 75% faster training than conditional DDPMs, validated through ablation studies and comparative analyses against astrostatistical/ML baselines.\n\nClarity: The paper is systematically structured, clearly outlining the problem setup, technical designs and evaluation metrics. Pictures and tables effectively communicate results.\n\nSignificance: The work shows that learning a full distributional trajectory can deliver stronger OOD robustness and lower training cost than conventional conditional diffusion or direct regression, with clear impact for scientific machine learning.\n\nWeaknesses:\n\n1. Incomplete physical modeling: The Astro-DSB framework does not explicitly encode the full forward physical equations governing GMC evolution. This limits its interpretability as a physics-driven model, as the learned dynamics may not fully align with underlying astrophysical laws. \n2. Limited OOD scenario validation: While OOD testing uses different MHD codes (ENZO vs. ORION2), the study focuses on specific initial conditions. It lacks validation across broader physical parameter spaces.\n\nQUESTIONS:\n1. Could analytic or learned physical drifts be inserted into the bridge to improve interpretability and extrapolation?\n2. What exactly delivers the four-fold training-time speed-up over the cDDPM baseline (shorter schedule, faster convergence, architectural changes)?\n3. Do multiple stochastic samples yield meaningful uncertainty estimates for astronomers, or is the output effectively deterministic?\n\nLIMITATIONS:\n1. The dynamics are purely data-driven. Conservation laws and intermediate physical states are not enforced.\n2. Iterative sampling can be slow for large-scale deployment without further acceleration or distillation.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}