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REVIEW 3 major objections 5 minor 87 references

Beyond the Proxy: Trajectory-Distilled Guidance for Offline GFlowNet Training

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read TD-GFN trains offline GFlowNets without a proxy: distilled edge rewards guide DAG pruning and backward sampling, gradient updates use only ground-truth terminal rewards, and the paper reports faster convergence with higher-quality samples…

desk verdict A useful offline training recipe whose central claim—that IRL edge rewards can guide the policy without contaminating it—is plausible but not proven; the mechanism needs a sharper argument or a targeted experiment. read the letter →

arxiv 2505.20110 v3 pith:RDF2K5EL submitted 2025-05-26 cs.LG cs.AI

Ruishuo Chen , Xun Wang , Rui Hu , Zhuoran Li , Longbo Huang This is my paper · ORCID
classification cs.LGcs.AI
keywords GenerativeFlowNetworksofflinetrainingproxy-freelearninginversereinforcementedgerewardsDAGpruningbackwardsamplingmoleculedesign
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

TD-GFN is a training framework for Generative Flow Networks (GFlowNets) that learns from a fixed set of reward-labeled trajectories without fitting a proxy reward model. The paper's central claim is that transition-level edge rewards distilled from those trajectories by inverse reinforcement learning can guide exploration better than the coarse constraints used by earlier proxy-free methods. To keep the policy robust, these learned rewards are not fed into the loss; they are used only to prune low-value edges from the environment DAG and to bias backward sampling of training trajectories, so every gradient update is computed from ground-truth terminal rewards. The paper reports that on hypergrid, antimicrobial peptide design, and molecule design, TD-GFN converges faster, finds more high-reward modes, and matches an oracle-reward GFlowNet using roughly twenty times fewer training trajectories. If correct, this makes offline GFlowNet training substantially more reliable in settings where reward queries are expensive or impossible.

What carries the argument

The central object is the transition-level edge reward $R_E(s,s')$ on the environment DAG, learned by adversarial imitation from a rebalanced offline dataset and converted from the discriminator output by the logit transform $R_E(s,s') = \log D_\phi(s,s') - \log(1 - D_\phi(s,s'))$ so that negative values are allowed. The machinery has two uses. First, the reward-guided pruning rule removes an edge when $R_E(s,s') < \mathrm{mean}(D_{R_E}) - K \cdot \mathrm{std}(D_{R_E})$, producing a smaller action space. Second, the backward policy $P_B(s_t \mid s_{t+1}) \propto \exp\{R_E(s_t, s_{t+1})\}$ over the pruned graph samples training trajectories backward from high-reward terminals. The theoretical bridge is the established equivalence between GFlowNet training and entropy-regularized reinforcement learning, which justifies applying IRL to edge-level quantities; the practical effect is that the policy receives dense guidance without any learned reward entering its loss.

What would settle it

Take a small DAG with two routes to a high-reward terminal, one common and one rare in the offline dataset, make the behavior policy's preferences oppose the reward landscape so that inverse reinforcement learning assigns higher edge rewards to the low-reward route, and check whether TD-GFN's pruning removes the rare high-reward edges; if the final policy's reward distribution is materially worse than pruning with ground-truth edge importance, the claim that inaccurate edge rewards cannot propagate into training is falsified.

Watch

Extended reading notes

Core claim

On its own terms, the paper discovers that the unequal importance of edges in a GFlowNet's environment DAG can be extracted as an edge-reward function from offline trajectories using maximum-causal-entropy inverse reinforcement learning on a reward-rebalanced dataset. These edge rewards are then used only indirectly: edges with rewards below a threshold are pruned from the DAG, and training trajectories are generated backward from reward-proportional terminal states using a softmax over edge rewards. The paper's key assertion is that because the rewards never enter the GFlowNet loss, the policy gradients depend only on recorded ground-truth terminal rewards, insulating the policy from proxy-style error propagation while still providing dense structural guidance. Empirically, the paper claims this yields the fastest convergence and best sample quality among the compared offline-GFlowNet and offline-RL baselines on all three benchmarks.

Load-bearing premise

The load-bearing premise is that the transition-level scores learned from the offline data are accurate enough that pruning and backward sampling do not systematically throw away paths to high-reward ends; if a wrong score removes or de-emphasizes the very paths that lead to the best outcomes, the final policy is still trained on ground-truth rewards but only over a biased subset of trajectories.

Editorial extensions

If this is right

  • If TD-GFN's claim holds, offline GFlowNet training no longer requires a proxy reward model, removing the main source of out-of-distribution reward-query errors.
  • The learned edge rewards generalize to transitions not present in the dataset, enabling discovery of high-reward modes beyond the support of the offline trajectories.
  • On the molecule-design benchmark, TD-GFN converges in roughly $2.75\times10^4$ training trajectories, about twenty times fewer than Oracle-GFN's $4.41\times10^5$, with comparable or better top-$k$ rewards.
  • The framework is agnostic to the downstream training objective: flow matching and trajectory balance both work after trajectory collection, and an offline RL loss can be substituted as well.

Reading between the lines

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

  • A formal guarantee for the paper's core robustness claim would need an error bound showing that estimated edge rewards do not remove high-reward edges; without such a bound, the claimed insulation from error propagation rests on the empirical margins.
  • The same edge-reward guidance could be run online, pruning the DAG dynamically from the agent's own experience; the paper lists this as a future direction, so it is an extension, not a paper claim.
  • A soft alternative to hard pruning, such as reweighting policy logits by the learned edge rewards, would isolate whether the benefit comes from shrinking the action space or from the dense guidance itself; the ablation suggests the hard pruning specifically is doing important work.
  • The paper itself notes in its discussion that TD-GFN relies on trajectories carrying meaningful structure, since uniform reverse-generated trajectories degrade performance; this delimits the method to datasets whose edge sequences contain information beyond terminal rewards.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes Trajectory-Distilled GFlowNet (TD-GFN), a proxy-free method for training GFlowNets from offline trajectory datasets. TD-GFN first uses maximum causal entropy IRL (in a GAIL-style adversarial loop) on a reward-rebalanced dataset to learn dense edge-level rewards. These learned rewards are then applied indirectly: they are used to prune low-utility transitions from the environment DAG (Eq. 6) and to define a prioritized backward sampling distribution over the pruned graph (Eq. 7). The policy is trained with a GFlowNet objective (FM or TB) using only the ground-truth terminal rewards from the dataset. Experiments on Hypergrid, AMP design, and molecule design show that TD-GFN converges faster and achieves higher sample quality than existing proxy-free and proxy-based baselines, including COFlowNet, Dataset-GFN, GAIL, BC, CQL, IQL, Proxy-GFN, and Oracle-GFN. The paper claims that because the final gradient updates rely only on ground-truth terminal rewards, the learned edge rewards do not cause error propagation.

Significance. If the central claim is substantiated, TD-GFN would be a practically valuable contribution to offline GFlowNet training, as it avoids the need for a learned terminal-reward proxy while still providing dense structural guidance. The paper includes extensive experiments across three tasks, ablations of the main components (Appendix D.6), and a sensitivity analysis of the pruning threshold (Appendix D.4). The empirical results are generally convincing: TD-GFN consistently outperforms a wide range of baselines in both convergence speed and final sample quality. However, the load-bearing theoretical claim that indirect use of edge rewards 'prevents error propagation' is not supported by the analysis or experiments, and this is the main weakness of the manuscript.

major comments (3)
  1. [Section 3.2, Eq. (6)-(7), Algorithm 1] The assertion that indirect use of edge rewards 'insulates the policy' from IRL error is not justified. Although the final gradient updates use only ground-truth terminal rewards, the set of trajectories over which those updates are computed is determined by the learned edge rewards: pruning (Eq. 6) removes low-scoring edges from the DAG, and backward sampling (Eq. 7) weights trajectories by softmax of edge rewards. An inaccurate edge-reward estimate can therefore remove or de-emphasize edges that lead to high-reward terminals, biasing the training distribution before any ground-truth gradient is applied. The paper provides no bound or experiment that isolates this failure mode; the ablations in Appendix D.6 show the components matter, but they do not demonstrate robustness to misestimated edge rewards. This is a load-bearing issue because the central claim of the paper is that error propagation is prevented.
  2. [Section 3.1, Eq. (4)-(5)] The rebalancing scheme P(τ) ∝ R(s_T) is introduced as an ad-hoc approximation of expert behavior, and the edge rewards are learned from the same offline dataset that is later used for policy training. The paper claims strong generalization of edge rewards to unobserved transitions, but the only evidence is the qualitative visualization in Appendix D.3 and favorable downstream performance. Because pruning and backward sampling are applied to the full DAG (including edges never seen in the dataset), the method's success hinges on the accuracy of the learned edge rewards on unobserved regions. This is neither theoretically analyzed nor systematically tested. A concrete experiment that corrupts or ablates a subset of learned edge rewards would help establish whether the indirect guidance mechanism is as robust as claimed.
  3. [Table 1 and Section 4.3] The comparison between TD-GFN and the offline RL baselines CQL and IQL is not apples-to-apples: the table reports only the best-performing seed for CQL and IQL, while all other methods report mean ± standard deviation over three seeds. This can artificially inflate the performance gap. Additionally, the '20 times fewer trajectories' claim relative to Oracle-GFN relies on a convergence metric that is not precisely defined in the main text; the reader should be told how convergence is measured and whether the comparison accounts for the fact that Oracle-GFN uses a pre-trained oracle model (trained on 300k molecules) as its reward source.
minor comments (5)
  1. [Section 4.1 and Appendix D.7] Equation (8) (the FM objective) is referenced in Section 4.1 but is only defined in Appendix D.7. It should be introduced in the main text or the cross-reference made more prominent, since the main experiments are run with this objective.
  2. [Section 4.2] The description of the AMP dataset is slightly unclear: the text says 'we train a Proxy-GFN and compare its performance', but the dataset description mentions two datasets (one for training a reward proxy and another for an oracle). Clarify how many datasets are used and which trajectories are provided to TD-GFN.
  3. [Section 4.3 and Related Work (Appendix B)] The paper does not include RO-GFlowNets (Wang et al., 2023) in the experimental comparison, despite it being the earliest proxy-free GFlowNet method and being mentioned in the related work. Since the paper claims state-of-the-art performance, a comparison or a clear explanation for its omission is needed.
  4. [Section 4.3 and Figure 1] The 'Convergence' metric in Table 1 and Figure 1 is not defined. State explicitly what constitutes 'performance convergence' (e.g., reaching a fixed number of modes or a threshold on top-k reward) so that the reader can interpret the reported speedup.
  5. [Appendix D.4] The sensitivity analysis of the pruning threshold K uses a tuning criterion ('highest ratio of retained recorded transitions to retained randomly selected transitions') that is not described in the main text. Briefly explain this criterion when first mentioning K in Section 3.2 or Appendix D.4.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: final GFlowNet updates use ground-truth terminal rewards; learned edge rewards enter only as data shaping.

full rationale

I traced the derivation chain. Edge rewards are extracted by GAIL on a rebalanced dataset (Eqs. 4-5), then used to prune the DAG (Eq. 6) and to define backward sampling (Eq. 7). Phase 3 samples terminals proportionally to recorded rewards and optimizes the policy with the FM or TB objective using those ground-truth terminal rewards (Eqs. 8-9). There is no equation-level reduction: learned edge rewards do not appear in the final loss, and the target distribution is not defined in terms of them. Inaccurate edge rewards could bias the support of training trajectories, but that is an unverified robustness assumption, not a self-referential derivation. The paper's own ablations and discussion acknowledge sensitivity to trajectory quality. Self-citations appear only in related work and metric references and are not load-bearing. No specific circular step can be quoted.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

No new physical or formal entities are postulated. The 'edge reward' is a learned function on the environment graph, not an unexplained construct. The main load-bearing assumptions are the equivalence to entropy-regularized RL, the pseudo-expert rebalancing, and the untested generalization of edge rewards to unobserved transitions.

free parameters (1)
  • Pruning threshold K = Hypergrid: 7.0; Molecule Design: 1.0; Biosequence Design: 2.0
    Tuned per task by selecting the value with the highest ratio of retained recorded transitions to retained randomly selected transitions (Appendix C.4, D.4). K directly controls which edges survive in the pruned DAG, a core component of TD-GFN.
assumptions (7)
  • standard math GFlowNet training is equivalent to entropy-regularized RL with gamma=1, lambda=1 and the modified reward in Eq (1).
    Invoked in Section 2.1 and used to justify applying IRL to GFlowNet edge rewards; this is a cited result from Tiapkin et al. (2024).
  • standard math Maximum causal entropy IRL (Eq 3) and the GAIL objective (Eq 4) recover a reward that explains the expert behavior, and the logit transform in Eq (5) yields an unbiased edge reward.
    Used in Section 3.1 to justify extracting edge rewards from the discriminator; relies on Ziebart et al. (2008; 2010), Ho and Ermon (2016), Kostrikov et al. (2018).
  • ad hoc to paper Reweighted trajectories P(tau) proportional to R(s_T) approximate an expert policy's visitation distribution.
    Introduced in Section 3.1 as a pseudo-expert dataset rebalancing strategy; no proof that this reweighting yields the true expert distribution.
  • domain assumption Edge rewards learned on observed transitions generalize meaningfully to unobserved transitions.
    Needed for pruning to retain unobserved high-reward pathways (Section 3.2, Appendix D.3); the paper provides visual evidence but no formal or statistical guarantee.
  • ad hoc to paper Edges with RE below mean(D_RE)-K*std(D_RE) are low-utility and can be pruned without losing important high-reward paths.
    This is the pruning rule in Eq (6); it is a heuristic threshold with no preservation guarantee, and K is tuned per task.
  • domain assumption The backward policy PB(s_t | s_{t+1}) proportional to exp{RE(s_t, s_{t+1})} is consistent with reward shaping and with the GFlowNet objective.
    Used in Eq (7) to sample training trajectories; consistency is stated but not derived in the paper.
  • domain assumption The environment has deterministic dynamics and a DAG structure as in standard GFlowNet settings.
    Stated in Section 2.1; the method's graph pruning and backward sampling rely on this structure.

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Cite this review

Pith. "Pith review of Beyond the Proxy: Trajectory-Distilled Guidance for Offline GFlowNet Training." pith.science (2026). https://pith.science/paper/RDF2K5EL

@misc{pith2026250520110,
  author       = {Pith},
  title        = {Pith review of: Beyond the Proxy: Trajectory-Distilled Guidance for Offline GFlowNet Training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RDF2K5EL}},
  note         = {Machine review of arXiv:2505.20110}
}
read the original abstract

Generative Flow Networks (GFlowNets) excel at sampling diverse, high-reward objects. In many practical applications where active reward queries are infeasible, these models must be trained using static offline datasets. Prevailing training methods typically rely on a proxy model to provide reward feedback for online sampled trajectories. However, constructing a reliable proxy is often challenging due to data scarcity or high evaluation costs. While existing proxy-free approaches attempt to address this, they often impose coarse constraints that limit the model's ability to explore effectively. To overcome these limitations, we propose Trajectory-Distilled GFlowNet (TD-GFN), a novel proxy-free training framework. TD-GFN utilizes inverse reinforcement learning (IRL) to extract dense, transition-level edge rewards from offline trajectories, providing rich structural guidance for efficient exploration. Crucially, to ensure robustness, these rewards guide the policy indirectly through DAG pruning and prioritized backward sampling. This design ensures that gradient updates rely exclusively on ground-truth terminal rewards from the dataset, thereby preventing error propagation. Empirical results demonstrate that TD-GFN significantly outperforms a broad range of existing baselines in both convergence speed and sample quality, establishing a more robust and efficient paradigm for offline GFlowNet training.

Figures

Figures reproduced from arXiv: 2505.20110 by the authors.

Figure 1
Figure 1. Comparison of methods on the Molecule Design task using a 1, 500-trajectory dataset. Top￾10 Reward is the average of the 10 best samples, and Convergence is the number of training tra￾jectories required for convergence. We compare against two proxy-based baselines from Bengio et al. (2021): Proxy-GFN (using a proxy learned on this dataset) and Oracle-GFN (using the oracle as a best-case proxy). See Section 4.3 for d… view at source ↗
Figure 2
Figure 2. Illustration of our motivation. All subfigures depict an environment DAG, where solid [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. An overview of the complete training pipeline of the TD-GFN framework. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: Performance comparison on the 8 4 Hypergrid task. The top row shows results using 1, 500 trajectories from the Expert and Mixed datasets for policy training, while the bottom row shows results using only 150 trajectories. The solid line and shaded region represent the …
Figure 5
Figure 5. Figure 5: Performance comparison on the 8 4 Hypergrid task. Policies are trained using the Median and Bad datasets, each consisting of 1, 500 trajectories. 4.2 BIOSEQUENCE DESIGN We next evaluate TD-GFN on a more challenging task—designing anti-microbial peptides (AMPs), i.e., s…
Figure 6
Figure 6. Figure 6: Comparison of reward and diversity among the top [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Number of high-reward modes (reward > 7 and > 7.5) discovered during training in the Molecule Design task. Notably, the powerful guidance provided at inter￾mediate steps allows TD-GFN to match Oracle￾GFN’s performance using 20 times fewer tra￾jectories, while also deci…
Figure 8
Figure 8. Figure 8: In this setting, algorithms are prone to overfitting due to the limited data. For example, both [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: Performance comparison on the 204 Hypergrid task using 1, 500 trajectories from four types of datasets. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: (c) shows the pruned DAG based on the edge rewards in [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 11
Figure 11. Figure 11: Performance comparison between different values of the pruning coefficient [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: Performance comparison with and without dataset rebalancing on [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]
Figure 13
Figure 13. Figure 13: Ablation study on the Mixed dataset. We evaluate three TD-GFN variants: (i) no pruning; (ii) dataset-based pruning that removes unseen edges; and (iii) uniform backward sampling from terminal nodes. Each TD-GFN component proves essential for achieving optimal performa…
Figure 14
Figure 14. Figure 14: Performance comparison of TD-GFN with different training objectives as well as [PITH_FULL_IMAGE:figures/full_fig_p025_14.png]
Figure 15
Figure 15. Figure 15: Performance of GFlowNet and CQL with and without our Trajectory-Distilled (TD) [PITH_FULL_IMAGE:figures/full_fig_p026_15.png]
Figure 16
Figure 16. Figure 16: Number of high-reward modes discovered by QM-TD-GFN compared to TD-GFN. [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]
Figure 17
Figure 17. Figure 17: Performance comparison on the 8 4 Hypergrid task. The top row uses 1, 500 trajectories from the Expert and Mixed datasets for policy training, while the bottom row uses only 150 trajecto￾ries. explicitly constrains policy actions to remain close to the data by penaliz…
Figure 18
Figure 18. Figure 18: Performance comparison of TD-GFN policies trained on the [PITH_FULL_IMAGE:figures/full_fig_p029_18.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.