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arxiv: 2605.12112 · v1 · submitted 2026-05-12 · 💻 cs.CV

Recognition: no theorem link

When Policy Entropy Constraint Fails: Preserving Diversity in Flow-based RLHF via Perceptual Entropy

Xiaofeng Tan , Jun Liu , Bin-Bin Gao , Yuanting Fan , Xi Jiang , Chengjie Wang , Hongsong Wang , Feng Zheng
Authors on Pith no claims yet

Pith reviewed 2026-05-13 05:45 UTC · model grok-4.3

classification 💻 cs.CV
keywords RLHFflow matchingperceptual entropydiversity collapsetext-to-imagepolicy gradiententropy regularizationgenerative models
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The pith

In flow-based RLHF for text-to-image models, policy entropy remains constant while perceptual diversity collapses, requiring perceptual entropy constraints to restore balance.

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

The paper argues that RLHF fine-tuning of flow-matching text-to-image models causes diversity to collapse in the space of human perception. Standard policy entropy fails to detect or prevent this because it stays fixed due to the unchanging noise schedule in flow models. The collapse stems instead from policy gradients that concentrate probability on high-reward modes. Perceptual entropy is defined to measure spread in perceptual feature spaces and is used to add regularization terms that keep the model from narrowing too much. Experiments on multiple models and rewards confirm that these perceptual constraints improve the trade-off between image quality and variety.

Core claim

The central discovery is that policy entropy in flow models does not change during RLHF because of the fixed noise schedule, even as the generated images lose perceptual diversity through mode-seeking optimization. Perceptual entropy is proposed as an alternative that tracks diversity in perceptual spaces while satisfying entropy axioms. This leads to two methods, Perceptual Entropy Constraint and Perceptual Constraints on Generation Space, which are shown to enhance both quality and diversity metrics in practice.

What carries the argument

Perceptual entropy, computed as the entropy of the policy distribution projected or evaluated in a perceptual embedding space.

If this is right

  • Perceptual Entropy Constraint yields the highest quality-diversity score of 0.734 compared to the baseline of 0.366.
  • Combining it with other constraints achieves an average diversity of 0.989 against the baseline's 0.047.
  • The gains hold consistently for two different base models, both neural and rule-based reward models, and three perceptual spaces.
  • Standard policy entropy regularization cannot prevent the model from converging to narrow high-reward regions in perceptual space.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar constant-entropy behavior may limit standard regularization in other flow or diffusion generative models during preference alignment.
  • Extending perceptual spaces to include semantic or stylistic features could further tailor diversity preservation to specific applications.

Load-bearing premise

The chosen perceptual spaces will continue to reflect meaningful diversity that aligns with human preferences across different tasks and models without causing unintended reductions in other qualities.

What would settle it

Training the model with the proposed perceptual constraints and measuring no corresponding increase in diversity according to independent perceptual metrics or human studies would show that the constraints do not achieve the intended preservation.

Figures

Figures reproduced from arXiv: 2605.12112 by Bin-Bin Gao, Chengjie Wang, Feng Zheng, Hongsong Wang, Jun Liu, Xiaofeng Tan, Xi Jiang, Yuanting Fan.

Figure 1
Figure 1. Figure 1: Diversity Collapse. Flow-GRPO improves quality but sacrifices diversity, producing similar styles. However, revisiting this intuition under flow matching reveals a key inconsistency: diversity collapses while the policy entropy surrogate remains constant, as shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Training-time Metrics. (a) Entropy vs. variance in VAE space. (b) Variance in pixel and reward space. Beyond the theoretical analysis, we empirically verify the constant policy entropy property in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Optimization Behavior. GRPO shows mode￾seeking behavior and converges to a single-peak distri￾bution with high reward, while an ideal model should encourage coverage of multiple high-reward regions. 0 200 400 600 800 Training Step 1.0 2.0 £ 1 0 ¡ 2 Std(R(© xªK k )) Var(© xªK k ) 0.75 1.50 £ 1 0 ¡ 2 0 200 400 600 800 Training Step 0.3 0.4 0.5 max© pA(x k)ªK k = 1 min© pA(x k)ªK k = 1 [PITH_FULL_IMAGE:figur… view at source ↗
Figure 5
Figure 5. Figure 5: Relationship between Reward and Perceptual Entropy. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimization Comparison. (a) Native KL (red) versus KL-as￾reward (blue), showing reward and entropy dynamics; (b) entropy with (blue) and without (red) JPCVAE. As illustrated in Fig.6, our method effectively mitigates these optimization issues. Com￾pared to Native KL, which introduces competing gradients, perceptual reward shaping aligns perceptual constraints with the primary objective and stabilizes trai… view at source ↗
Figure 7
Figure 7. Figure 7: Training Dynamics of Flow-GRPO, Flow￾GRPO with KL, and PEC with Perceptual Entropy. (a) Mean reward. (b) Reward standard deviation. Trade-Off between Diversity and Quality [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

RLHF is widely used to align flow-matching text-to-image models with human preferences, but often leads to severe diversity collapse after fine-tuning. In RL, diversity is often assumed to correlate with policy entropy, motivating entropy regularization. However, we show this intuition breaks in flow models: policy entropy remains constant, even while perceptual diversity collapses. We explain this mismatch both theoretically and empirically: the constant entropy arises from the fixed, pre-defined noise schedule, while the diversity collapse is driven by the mode-seeking nature of policy gradients. As a result, policy entropy fails to prevent the model from converging to a narrow high-reward region in the perceptual space. To this end, we introduce perceptual entropy that captures diversity in a perceptual space and maintains the property of standard entropy. Building upon this insight, we propose two entropy-regularized strategies, Perceptual Entropy Constraint and Perceptual Constraints on Generation Space, to preserve perceptual diversity and improve the quality. Experiments across two base models, neural and rule-based rewards, and three perceptual spaces demonstrate consistent gains in the quality-diversity trade-off; PEC achieves the best overall score of 0.734 (vs. baseline's 0.366); a complementary setting of PEC further reaches a diversity average of 0.989 (vs. baseline's 0.047). Our project page (https://xiaofeng-tan.github.io/projects/PEC) is publicly available.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that standard policy entropy regularization fails to preserve diversity in flow-matching text-to-image RLHF because policy entropy remains constant (due to the fixed pre-defined noise schedule) while perceptual diversity collapses (due to mode-seeking policy gradients). It introduces perceptual entropy as a diversity measure in perceptual spaces that preserves standard entropy properties, and proposes two regularization strategies—Perceptual Entropy Constraint (PEC) and Perceptual Constraints on Generation Space—to improve the quality-diversity trade-off, with experiments across two base models, neural/rule-based rewards, and three perceptual spaces reporting gains such as 0.734 vs. baseline 0.366 overall score and 0.989 vs. 0.047 diversity average.

Significance. If the claimed mismatch between constant policy entropy and collapsing perceptual diversity is rigorously established and the perceptual entropy constraints generalize without side effects, the work would be significant for RLHF in flow-based generative models, offering a targeted fix for diversity collapse that standard entropy regularization cannot address. The multi-setting empirical evaluation and public project page provide some support for practical utility and reproducibility.

major comments (2)
  1. [Abstract / theoretical analysis] Abstract and theoretical explanation: The central claim that policy entropy remains constant due to the fixed noise schedule does not engage with the change-of-variables formula for differential entropy under a learned flow. In flow-matching models the output entropy equals base entropy plus the integral of the divergence of the time-dependent vector field along trajectories; RLHF updates to the vector field should therefore alter output entropy unless the divergence is provably invariant, which is not shown.
  2. [Method] Method section on perceptual entropy: The definition of perceptual entropy is stated to 'capture diversity in a perceptual space and maintain the property of standard entropy,' yet no explicit functional form, proof of non-negativity or concavity, or comparison to the standard differential entropy appears. Without these, it is unclear whether the quantity is independent of the reward model or reduces to a fitted heuristic, weakening the justification for the proposed constraints.
minor comments (2)
  1. [Experiments] Experiments: Reported aggregate scores (0.734 vs. 0.366; 0.989 vs. 0.047) are given without error bars, number of random seeds, or statistical tests, making it impossible to judge whether the quality-diversity improvements are reliable.
  2. [Abstract] Abstract: The two proposed strategies are named but not briefly characterized, which would improve immediate readability for readers scanning the contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below with clarifications on our theoretical analysis and definitions. Where the comments identify gaps in rigor or explicitness, we indicate that revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract / theoretical analysis] Abstract and theoretical explanation: The central claim that policy entropy remains constant due to the fixed noise schedule does not engage with the change-of-variables formula for differential entropy under a learned flow. In flow-matching models the output entropy equals base entropy plus the integral of the divergence of the time-dependent vector field along trajectories; RLHF updates to the vector field should therefore alter output entropy unless the divergence is provably invariant, which is not shown.

    Authors: We appreciate the referee's observation regarding the change-of-variables formula. In our analysis, 'policy entropy' specifically denotes the entropy of the fixed base noise distribution at the input to the flow, which is invariant because the noise schedule is pre-defined and unchanged by RLHF updates to the vector field. The perceptual diversity collapse, by contrast, arises from the mode-seeking behavior of the policy gradient in the output space. We acknowledge that a full accounting of output differential entropy must incorporate the divergence integral. In the revised manuscript we will expand the theoretical section to explicitly reference the change-of-variables formula, derive the relationship between input entropy and perceptual-space diversity under our RLHF objective, and discuss why the divergence term does not counteract the observed mode collapse in practice. This will strengthen the justification for why standard policy-entropy regularization is insufficient. revision: yes

  2. Referee: [Method] Method section on perceptual entropy: The definition of perceptual entropy is stated to 'capture diversity in a perceptual space and maintain the property of standard entropy,' yet no explicit functional form, proof of non-negativity or concavity, or comparison to the standard differential entropy appears. Without these, it is unclear whether the quantity is independent of the reward model or reduces to a fitted heuristic, weakening the justification for the proposed constraints.

    Authors: We thank the referee for noting the need for greater formality. Perceptual entropy is defined as the differential entropy of the push-forward distribution of generated samples under a fixed perceptual embedding map (e.g., CLIP or VGG features). Its explicit form is H_perp = -E_{x~p_gen}[log p_perp(f(x))], where f is the embedding function and p_perp is the density estimated in the perceptual space; because the embedding is fixed and independent of the reward model, the quantity inherits non-negativity and concavity from standard differential entropy on the embedded manifold. In the revised method section we will state this functional form explicitly, include a short derivation confirming the inherited properties, and add a comparison paragraph showing that it reduces to ordinary differential entropy when the perceptual map is the identity. These additions will clarify that the measure is not a fitted heuristic and directly supports the proposed PEC and generation-space constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims rest on model structure and new perceptual measure rather than self-referential fits or citations

full rationale

The paper's derivation of constant policy entropy from the fixed noise schedule in flow-matching models is presented as a direct consequence of the generative process definition (base distribution plus learned transport), not a renaming or fit of the target diversity quantity. Perceptual entropy is introduced as an explicit new functional on chosen perceptual embeddings that is stated to preserve entropy-like properties; this is a definitional extension rather than a reduction of the output to the input by construction. No load-bearing self-citation chains, uniqueness theorems from the same authors, or fitted parameters relabeled as predictions appear in the abstract or described chain. Experiments across models and spaces supply independent empirical content. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on domain assumptions about flow model dynamics and introduces perceptual entropy as a new measure; insufficient detail to list specific fitted parameters.

axioms (2)
  • domain assumption Policy entropy in flow models remains constant due to the fixed pre-defined noise schedule
    Invoked to explain why standard entropy regularization fails to prevent diversity collapse.
  • domain assumption Diversity collapse is driven by the mode-seeking nature of policy gradients
    Used to account for the observed perceptual narrowing despite constant entropy.
invented entities (1)
  • perceptual entropy no independent evidence
    purpose: Captures diversity in a perceptual space while maintaining the mathematical properties of standard entropy
    New quantity introduced to replace or augment policy entropy for regularization in flow-based RLHF.

pith-pipeline@v0.9.0 · 5579 in / 1551 out tokens · 143469 ms · 2026-05-13T05:45:26.678221+00:00 · methodology

discussion (0)

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