The Flexibility Trap: Why Arbitrary Order Limits Reasoning Potential in Diffusion Language Models

Abstract: Diffusion LLMs (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential for general tasks like mathematics and coding. Consequently, numerous works have leveraged reinforcement learning (RL) to elicit the reasoning capability of dLLMs. In this paper, we reveal a counter-intuitive reality: arbitrary order generation, in its current form, narrows rather than expands the reasoning boundary of dLLMs. We find that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, leading to a premature collapse of the solution space. This observation motivates a rethink of RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We demonstrate that effective reasoning can be better elicited by intentionally forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, JustGRPO, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs. Project page: https://nzl-thu.github.io/the-flexibility-trap

• The paper demonstrates that enforcing autoregressive constraints instead of arbitrary order expands the reasoning solution space, as shown by higher Pass@k scores.
• It employs rigorous experiments on GSM8K, MATH, and other benchmarks to reveal that AR decoding overcomes entropy degradation at critical reasoning junctures.
• The study introduces JustGRPO, a framework that optimally balances RL training with maintained parallel decoding, resulting in enhanced reasoning performance and faster inference.

The Flexibility Trap in Diffusion LLMs: Autoregressive Constraints Enhance Reasoning

Introduction

Diffusion LLMs (dLLMs) have generated significant research interest due to their ability to break free from the strict left-to-right (autoregressive, AR) token generation paradigm by enabling arbitrary-order and parallel token sampling. While dLLMs offer substantial speedups in inference via parallelism, the presumed benefit of arbitrary generation order for complex reasoning tasks has motivated the design of increasingly complex reinforcement learning (RL) protocols tailored to leverage this flexibility. In "The Flexibility Trap: Why Arbitrary Order Limits Reasoning Potential in Diffusion LLMs" (2601.15165), the authors provide a rigorous and counter-intuitive critique of this central assumption. They demonstrate that, in practice, arbitrary order does not expand—indeed, it often restricts—the reasoning solution manifold of dLLMs, and that standard autoregressive constraints during training unlock superior reasoning capacity.

Theoretical Framing: Reasoning Potential and Exploration

The central proxy for reasoning capacity is Pass@$k$: the probability that at least one correct solution is found among $k$ independent samples. In the context of RL with Verifiable Rewards (RLVR), enhanced exploration and coverage of solution space is critical—good RL training relies on positive exploration signals being present in the model's sampling distribution. Therefore, higher Pass@$k$ directly reflects a model's inherent capacity for learning complex reasoning behaviors through RL post-training.

Arbitrary Order’s Surprising Limitation on Reasoning

Despite theoretical expectations that the arbitrary-order generation of dLLMs would allow richer, non-sequential exploration of reasoning paths—particularly for math and code generation tasks—the empirical evidence presented contradicts this intuition. Restricting dLLMs to AR order not only does not harm, but actually expands, the reachable reasoning solution space—leading to consistently higher Pass@$k$ scores across GSM8K, MATH, and programming benchmarks.

Figure 1: Restricting dLLMs to the standard AR decoding order expands the solution space available for reasoning and enables effective elicitation with standard GRPO.

The empirical profiles show that while arbitrary-order generation is competitive in single-shot (k=1) settings, it exhibits substantially worse solution scaling as $k$ increases, as shown by consistently lower Pass@$k$ curves.

Figure 2: Pass@$k$ as a function of $k$ reveals flatter scaling for arbitrary order, indicating restricted solution diversity relative to AR generation.

A detailed solution coverage analysis found that the solution manifold reached under arbitrary-order generation is essentially a strict subset of that available to AR order decoding: AR recovers significant numbers of solutions unattainable by arbitrary order, while the reverse is negligible.

Mechanistic Analysis: Entropy Degradation via Fork Bypass

The core mechanism underlying this "flexibility trap" is the model's adaptive handling of uncertainty during generation. In AR decoding, high-entropy "forking tokens" (often logical connectives or reasoning junctures) must be confronted and resolved as they are encountered, preserving local uncertainty and supporting exploration across divergent reasoning paths. Arbitrary-order strategies, however, systematically bypass these hard tokens, opting to fill in low-entropy, high-certainty positions first.

Figure 3: Arbitrary-order decoding persistently bypasses logical connectors, deferring decisions at reasoning forks.

When the model returns to fill in these connectors, the surrounding bidirectional context has eliminated ambiguity, leading to a collapse in entropy—dubbed "entropy degradation." This eliminates the capacity to genuinely explore alternate reasoning chains from those critical junctures. Empirical entropy measurements confirm that, while global entropy remains similar, entropy at logical forks sharply decreases in arbitrary-order decoding compared to AR.

Figure 4: Direct measurements show dramatic entropy degradation at logical forks in arbitrary order, confirming premature solution space collapse.

Practical Complexity and the JustGRPO Solution

Preserving arbitrary order has deeply complicated RL for dLLMs: existing RL algorithms must address the combinatorial explosion of unmasking trajectories, rely on unstable likelihood surrogates, and endure token-level credit assignment ambiguities. By contrast, if reasoning potential is maximized under AR constraints, such complexity is unwarranted.

The proposed JustGRPO framework simply applies the standard Group Relative Policy Optimization (GRPO) to dLLMs, treating them as AR policies during RL training. This enables rigorous, tractable, and efficient optimization without sacrificing the inherent parallel decoding capabilities of dLLMs at inference time.

Experimental Results

Quantitative experiments on GSM8K, MATH, HumanEval, and MBPP confirm the core findings:

• On GSM8K, JustGRPO achieves 89.1% accuracy, a 3% absolute improvement over previous state-of-the-art RL for dLLMs.
• On MATH-500, JustGRPO improves by 6.1% compared to the strongest alternative diffusion RL protocol.

These gains are stable across varying sequence lengths, confirming that improvements derive from richer navigation of logic branches and not simply overfitting to trajectory length.

Parallel Decoding Remains Intact

A potential concern is that AR-constrained RL training might erode the parallel decoding benefits of dLLMs. However, empirical evaluation demonstrates that models trained with JustGRPO preserve efficient parallel decoding at inference. In fact, under more aggressive parallel generation schemes, JustGRPO models exhibit strictly superior speed-accuracy trade-offs, revealing that AR-based RL produces a more robust and generalizable reasoning manifold.

Figure 3: JustGRPO maintains—but even enhances—the parallel decoding capability and robustness to increased token parallelism.

Theoretical and Practical Implications

This work recasts the role of flexibility in dLLM reasoning. The naive embrace of arbitrary-order generation as a universal benefit for complex reasoning is empirically unfounded; flexibility is shown to be an exploitation mechanism that hinders, rather than helps, the RL-based discovery of strong reasoning policies. AR constraints during RL training provide both a theoretical and practical simplification, producing not only better reasoning accuracy but also more robust inference-time decoding.

For the broader pursuit of advanced, scalable, and efficient language modeling, this result motivates a return to basic, interpretable orderings for reasoning-intensive tasks. Future research on dLLMs may focus more acutely on disentangling the roles of parallelism vs. order, developing hybrid protocols that decouple reasoning structure from speed, and exploring selective or adaptive orderings only where they truly enhance exploration rather than restrict it.

Conclusion

By dissecting the interplay between generation order and reasoning in dLLMs, this study compels a significant re-evaluation of core algorithmic priorities in diffusion-based language modeling. Rather than embracing arbitrary flexibility as an unconditional good, training-time autoregressive constraints—in the context of modern RL with verifiable rewards—result in enhanced reasoning performance, a broader accessible solution space, and preserved inference-time parallelism. These findings advocate for minimalist and theory-aligned optimization in the development of next-generation dLLMs.