Object-centric Denoising Diffusion Models for Physical Reasoning

Andrew Melnik; Laurenz Wiskott; Moritz Lange; Raphael C. Engelhardt; Wolfgang Konen

REVIEW 4 major objections 5 minor 28 references

Object-centric Denoising Diffusion Models for Physical Reasoning

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper proposes an object-centric denoising diffusion architecture for physical reasoning that is translation equivariant over time, permutation equivariant over objects, and can be conditioned on arbitrary time steps for arbitrary…

desk verdict A novel conditioning mechanism for object-centric diffusion, but the headline multi-condition capability rests on qualitative examples and a hard-conditioning shift that is not dynamics-preserving for interacting objects. read the letter →

arxiv 2507.04920 v1 pith:XJQTJJEE submitted 2025-07-07 cs.LG cs.AI

Moritz Lange , Raphael C. Engelhardt , Wolfgang Konen , Andrew Melnik , Laurenz Wiskott This is my paper

classification cs.LGcs.AI

keywords object-centricdiffusiondenoisingmodelsphysicalreasoningtrajectorypredictionpermutationequivariancetranslationconditionalgenerationPHYRE

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a denoising diffusion model built around individual objects, rather than a flat scene vector, can solve physical reasoning tasks that autoregressive forward models cannot. Because diffusion generates every time step of every object's trajectory together, the model can be conditioned not only on initial states but also on goal states and on different time steps for different objects. The authors introduce an attention-convolution architecture that is translation equivariant over time (shifting the whole trajectory just shifts the prediction) and permutation equivariant over objects (swapping object labels leaves their trajectories unchanged), together with two conditioning mechanisms: masked linear-modulation soft conditioning, and hard conditioning that shifts predicted trajectories after each denoising step so specified states are met exactly. On a standard physical reasoning benchmark, the model places an otherwise unconstrained object so that conditions imposed on other objects are satisfied, and ablations show that removing the hard conditioning hurts accuracy more than removing either the interaction layer or the feature-processing layer. The sympathetic reading is that this design makes multi-condition physical reasoning tractable in a single generative model.

What carries the argument

The central object is the attention-convolution block (AC block), which combines a pointwise MLP, multihead self-attention over objects, and a 1D temporal convolution with zero padding. The attention gives permutation equivariance over objects, and the convolution gives translation equivariance over time, with a skip connection that lets the network discard interaction information when it is irrelevant. These blocks are stacked into residual blocks inside a U-Net. Conditioning is carried by two mechanisms: masked linear modulation, in which a learned condition network produces modulation factors and a continuous mask so conditions affect only designated objects and time steps, and trajectory shifting, in which the predicted trajectory of each conditioned object is translated after every denoising step by the difference at the conditioned time step, or by a linear interpolation between multiple condition differences. A modified training loss teaches the model to predict already-shifted trajectories, which is what makes the shifted samples match ground truth.

What would settle it

A concrete check would be to generate trajectories for three interacting objects with one object conditioned at both its initial and final states and another object left free, then count how often the trajectories after the shifting step contain object overlaps or abrupt velocity discontinuities; if these violations grow as the number of interacting objects or the distance between conditions grows, the assumption that shifting preserves physical plausibility would be refuted.

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Extended reading notes

Core claim

The central claim is that an object-centric denoising diffusion model, with an MLP for per-object features, multihead self-attention for interactions between all objects at each time step, and a 1D convolution for each object's temporal evolution, can generate full multi-object trajectories that satisfy arbitrary conditions at arbitrary time steps. The paper proposes soft conditioning, which injects conditions through masked linear modulation so only selected objects and time steps are affected, and hard conditioning, which shifts predicted trajectories after every denoising step so that all specified states are exactly met, with linear interpolation between multiple conditions on one object. In the authors' experiments, this model can take initial and final conditions for some objects and freely place another object so that the conditions are fulfilled, and the results indicate that hard conditioning is the largest single contributor to trajectory accuracy.

Load-bearing premise

The load-bearing premise is that after hard conditioning shifts a predicted trajectory to satisfy given states, the shifted trajectory remains physically plausible enough for the model to correct interaction errors in subsequent denoising steps; with interacting objects this is not guaranteed, and the paper supports it mainly with qualitative examples.

Editorial extensions

If this is right

Because all time steps are generated together, the model can be conditioned on goal states or any later time step, which autoregressive forward models cannot do without trial-and-error search.
The two equivariances allow a single trained model to run with different object counts and trajectory lengths at inference, although quality degrades as the trajectory length moves away from the training length.
Hard conditioning guarantees that generated trajectories obey all specified conditions exactly, and with multiple conditions on one object it transitions between them by linear interpolation.
Ablations show that removing hard conditioning degrades mean trajectory error more than removing either the object-interaction or feature-processing component, and the non-object-centric variant loses permutation equivariance and scales its weights with the number of objects.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The hard-shifting operation can be read as a differentiable projection onto the set of condition-satisfying trajectories, so a natural extension would be to apply the same anchoring to any diffusion trajectory model and to test whether iterative, interaction-aware corrections during denoising improve physical plausibility.
The paper reports that overlap-penalty and differentiable collision-correction losses failed to converge, which suggests that naive global penalties are not the right way to inject interaction constraints; contact-aware local corrections are a promising alternative to test.
If a benchmark with denser coverage of relative object positions existed, the paper's hypothesis that interaction generalization is limited by data coverage could be tested directly; the authors state that no such benchmark currently exists.
The degradation at non-training trajectory lengths is attributed to boundary effects in the temporal convolution, so padding strategies or learned boundary handling could extend the model to arbitrary horizons while preserving the equivariances.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper gives us a genuinely new object-centric U-Net for trajectory diffusion, with two conditioning tricks worth knowing: masked-FiLM soft conditioning and a trajectory-shifting hard conditioning. The combination lets you condition on arbitrary time steps for arbitrary objects, which autoregressive forward models and prior diffusion trackers like Ye et al. cannot do. The architecture is permutation equivariant over objects and translation equivariant over time, and the ablation actually shows the hard conditioning matters: removing it worsens RMSE noticeably. The authors are also honest: they state outright that shifting is not physical with interactions, that the model must iteratively correct the artifacts, and that their attempts at overlap-correction failed to converge. That transparency is real credit.

The soft spots are in the gap between what is claimed and what is measured. The main selling point—solving tasks with multiple conditions at arbitrary time steps—is supported only by Figures 1 and 3, which are qualitative. The quantitative RMSE experiments condition only on initial states. The trajectory-length analysis in §4.5 filters to RMSE < 0.15, i.e., best-case generations only, so it does not tell you how often the model fails. And the hard-conditioning shift is not dynamics-preserving: translating one object changes its position relative to all others, so collision times and forces in the shifted trajectory no longer match the unshifted objects. The paper acknowledges this and asserts the denoising process corrects it, but that assertion is undemonstrated. The failed overlap-correction work suggests such corrections are genuinely hard for this framework.

So: the reader's conditional verdict is right. The paper is not ready to be taken as evidence that object-centric diffusion solves multi-condition physical reasoning. But it is a serious, clearly-written technical contribution with a novel conditioning mechanism and open code. A good referee could turn it into a publishable paper by demanding quantitative multi-condition evaluation, comparisons against autoregressive baselines (e.g., sampling red-ball positions with a forward model), and unfiltered trajectory-length results. It deserves peer review, not desk rejection. I'd bring it to reading group because the conditioning method is instructive, but I wouldn't cite it yet for the multi-condition capability.

Referee Report

4 major / 5 minor

Summary. This paper proposes an object-centric denoising diffusion model for physical reasoning. The architecture is built from attention-convolution blocks that are permutation equivariant over objects and translation equivariant over time, and supports conditioning on arbitrary object states at arbitrary time steps. The authors introduce a soft conditioning method based on masked FiLM-style modulation and a hard conditioning method based on trajectory shifting. Experiments on PHYRE-based data evaluate trajectory prediction RMSE, ablations, generalization to different object numbers, and behavior under varying trajectory lengths. The paper's central claim is that the model can solve physical reasoning tasks with multiple conditions at arbitrary time steps, including free objects placed by the model.

Significance. The paper combines several established ideas in a clean architecture and releases its implementation. The component-wise ablations are useful, and the equivariance properties are valuable design choices. However, the quantitative evaluation does not address the central multi-condition claim, which is supported only by qualitative examples. The paper is a useful step but its main contribution needs stronger evidence.

major comments (4)

[Sections 4.1 and 4.2] Section 4.1 states that all RMSE evaluations condition only on initial states, while Section 4.2 supports the multi-condition claim with only qualitative examples (Figures 1 and 3). Section 4.5 further restricts the trajectory-length analysis to RMSE values below 0.15. Thus the paper's central claim that the model solves tasks where some objects are conditioned at multiple time steps while other objects are placed freely is never quantitatively evaluated. Please provide quantitative results for such multi-condition scenarios, including RMSE of the unconditioned objects, RMSE of the conditioned objects after accounting for the hard conditioning, and a comparison to a baseline such as inpainting or an autoregressive model.
[Section 3.2] Section 3.2 acknowledges that the hard-conditioning shift is not physical-plausibility-preserving for interacting objects, and argues that iterative denoising corrects the resulting errors. However, no quantitative evidence is given for this correction. The modified loss only encourages the raw prediction to equal the shifted prediction, which does not directly enforce physical consistency. The failed overlap-correction experiments reported in Section 5 suggest that enforcing physical consistency inside the denoising loop is nontrivial. Please report a quantitative analysis of the hard-conditioning mechanism, for example by measuring how the error of shifted trajectories evolves over denoising steps or by evaluating prediction quality on multi-condition tasks with interacting objects.
[Section 4.3] Section 4.3 compares only ablations of the proposed architecture (No hard conditioning, CNN only, No MLP) and does not include any external baseline. Without comparison to an autoregressive physical reasoning model or an existing trajectory diffusion model on the same benchmark, the claimed advantage over prior approaches is not established. Please include at least one autoregressive baseline and one diffusion-based baseline under the same initial-state-conditioning protocol.
[Section 4.1] Section 4.1 introduces fixed bars around scenes to replace the original PHYRE environmental bounds, which changes the environment dynamics. The paper justifies this as necessary for generalization but does not verify that models trained with this augmentation transfer to the original PHYRE tasks. Please report performance under the original PHYRE setup, or show that the augmentation does not systematically alter the evaluation.

minor comments (5)

[Section 3.1] The notation for denoising steps is described as 'denoting denoising diffusion steps with at', which is typographically odd; please use a clearer symbol and ensure it is used consistently.
[Figures 1 and 3] The captions of Figures 1 and 3 should state whether the displayed trajectories exactly satisfy the conditioned states by construction of the hard conditioning, rather than appearing to satisfy them only qualitatively.
[Section 3.2] The soft-conditioning mask M is described as a continuous value clipped to [0,1], but the paper does not specify how the mask networks are trained; please clarify the training signal for M, C_m, and C_b.
[Section 4.3] The sentence about the waist of the distribution being not a clear separation between scenarios with and without interactions is vague; consider describing the bimodality and its relation to object interactions more precisely.
[Appendix A.1] The RTI block diagram shows a sinusoidal time embedding, but the text does not describe how the diffusion time step is injected into the AC blocks beyond the diagram; please elaborate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: hard conditioning is a disclosed enforcement mechanism, not a learned prediction, and quantitative evaluation is against the external PHYRE simulator.

full rationale

The paper's central derivation is self-contained rather than circular. The hard-conditioning procedure in Section 3.2 shifts predicted trajectories so that specified states are met; the paper explicitly states, 'Resulting trajectories are always guaranteed to obey all conditions.' This is a disclosed algorithmic enforcement, not a hidden reduction of a learned prediction to its own input. The learned component is the denoising model that generates the rest of the trajectory, including free objects, and the training loss includes both a penalty for the shift and a term comparing the shifted trajectory to ground truth, so the model is trained to anticipate the anchoring operation rather than being trivially defined by it. Quantitative evaluation in Section 4.3 and Figure 4 measures RMSE against the external PHYRE simulator for initial-state-conditioned trajectories; satisfying the initial condition is enforced by construction, but the future trajectory is not forced and is scored against simulator output. The self-citations, primarily Melnik et al. (2023), are used for benchmark context and literature overview and are not load-bearing for the architecture, conditioning, or experimental claims. The multi-condition demonstrations in Figures 1 and 3 are qualitative and are drawn from training templates, which weakens the evidence for generalization, but that is a support gap rather than circularity. No equation or fitted parameter is renamed as a prediction, and no load-bearing uniqueness claim is imported from previous work by the same authors.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard diffusion machinery plus PHYRE as ground truth. The most load-bearing domain assumption is that trajectory shifting preserves physical plausibility; the paper itself acknowledges this is not guaranteed with interactions. One architectural detail (conditioning depth) was chosen empirically. No invented entities or fitted target quantities are used.

free parameters (1)

Number of residual blocks receiving conditioning = 2 (first two downsampling blocks)
Section 3.2 states this was found empirically to be sufficient; a hand-chosen architectural hyperparameter.

assumptions (5)

standard math Denoising diffusion probabilistic model theory and cosine noise schedule are correct and applicable to this setting.
The model is built on DDPM (Ho et al. 2020) and cosine schedule (Nichol and Dhariwal 2021), standard background.
domain assumption PHYRE simulator provides a valid ground-truth physics for training and evaluation.
All RMSE errors are computed against the simulator; if simulator dynamics do not represent the target physical reasoning task, conclusions change.
ad hoc to paper Adding fixed bars around scenes (boxing) does not alter the task in a way that invalidates the PHYRE-based evaluation.
The paper adds bars to replace the physically implausible border bouncing in PHYRE; this changes the environment and could affect interaction statistics at boundaries. The authors treat it as benign augmentation.
domain assumption Shifting generated trajectories to meet conditions preserves physical plausibility well enough that the denoising process can compensate for interaction errors.
Hard conditioning shifts the entire trajectory (or interpolates between multiple conditions) after every denoising step; the paper argues the model can iteratively correct for interaction violations, but this is only supported by qualitative examples.
domain assumption Object feature vectors rather than images are sufficient to learn physical interactions.
The model operates on pre-extracted object feature vectors, omitting visual input; this is a deliberate simplification that may not capture all information present in images.

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Cite this review

Pith. "Pith review of Object-centric Denoising Diffusion Models for Physical Reasoning." pith.science (2026). https://pith.science/paper/XJQTJJEE

@misc{pith2026250704920,
  author       = {Pith},
  title        = {Pith review of: Object-centric Denoising Diffusion Models for Physical Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XJQTJJEE}},
  note         = {Machine review of arXiv:2507.04920}
}

read the original abstract

Reasoning about the trajectories of multiple, interacting objects is integral to physical reasoning tasks in machine learning. This involves conditions imposed on the objects at different time steps, for instance initial states or desired goal states. Existing approaches in physical reasoning generally rely on autoregressive modeling, which can only be conditioned on initial states, but not on later states. In fields such as planning for reinforcement learning, similar challenges are being addressed with denoising diffusion models. In this work, we propose an object-centric denoising diffusion model architecture for physical reasoning that is translation equivariant over time, permutation equivariant over objects, and can be conditioned on arbitrary time steps for arbitrary objects. We demonstrate how this model can solve tasks with multiple conditions and examine its performance when changing object numbers and trajectory lengths during inference.

Figures

Figures reproduced from arXiv: 2507.04920 by the authors.

**Figure 2.** Attention-convolution block. The variables are defined as follows: [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Left: Provided conditions fix initial states of green ball and blue bar, and the final state of the green ball. The red ball has no conditions. Right: The denoising process. Figures 1 and 3 show examples where conditions at multiple time steps are provided for the green and blue objects, while there are no conditions for the red ball. These conditions are motivated by the PHYRE goal of making green and blue object… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Performance of model variants for trajectories of 3 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Results when training a model on all 25 templates simultaneously. Performance on train tasks is blue, performance [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Quality of generated trajectories for different tra [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Full architecture of our proposed denoising diffusion model, without conditioning modules. The values for parameters [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Ajay, A.; Du, Y.; Gupta, A.; Tenenbaum, J.; Jaakkola, T.; and Agrawal, P. 2022. Is Conditional Generative Modeling all you need for Decision - Making ? ArXiv:2211.15657 [cs]

arXiv 2022

[2] [2]

Bakhtin, A.; van der Maaten, L.; Johnson, J.; Gustafson, L.; and Girshick, R. 2019. PHYRE : A New Benchmark for Physical Reasoning . ArXiv:1908.05656 [cs, stat]

arXiv 2019

[3] [3]

Brody, S.; Alon, U.; and Yahav, E. 2021. How Attentive are Graph Attention Networks ?

work page 2021

[4] [4]

T.; Baierl, M.; Koert, D.; and Peters, J

Carvalho, J.; Le, A. T.; Baierl, M.; Koert, D.; and Peters, J. 2024. Motion Planning Diffusion : Learning and Planning of Robot Motions with Diffusion Models . ArXiv:2308.01557 [cs]

arXiv 2024

[5] [5]

Chan, S. H. 2024. Tutorial on Diffusion Models for Imaging and Vision . ArXiv:2403.18103

arXiv 2024

[6] [6]

Corneanu, C.; Gadde, R.; and Martinez, A. M. 2024. LatentPaint : Image Inpainting in Latent Space with Diffusion Models . In 2024 IEEE / CVF Winter Conference on Applications of Computer Vision ( WACV ) , 4322--4331. Waikoloa, HI, USA: IEEE. ISBN 979-8-3503-1892-0

work page 2024

[7] [7]

Daniel, T.; and Tamar, A. 2023. DDLP : Unsupervised Object -centric Video Prediction with Deep Dynamic Latent Particles . Transactions on Machine Learning Research

work page 2023

[8] [8]

Dhariwal, P.; and Nichol, A. 2021. Diffusion Models Beat GANs on Image Synthesis . In Advances in Neural Information Processing Systems , volume 34, 8780--8794. Curran Associates, Inc

work page 2021