Masked Diffusion Models (MDMs) have emerged as a promising non-autoregressive paradigm for generative tasks, offering parallel decoding and bidirectional context utilization. However, current sampling methods rely on simple confidence-based heuristics that ignore the long-term impact of local decisions, leading to trajectory lock-in where early hallucinations cascade into global incoherence. While search-based methods mitigate this, they incur prohibitive computational costs ($O(K)$ forward passes per step). In this work, we propose Backward-on-Entropy (BoE) Steering, a gradient-guided inference framework that approximates infinite-horizon lookahead via a single backward pass. We formally derive the Token Influence Score (TIS) from a first-order expansion of the trajectory cost functional, proving that the gradient of future entropy with respect to input embeddings serves as an optimal control signal for minimizing uncertainty. To ensure scalability, we introduce \texttt{ActiveQueryAttention}, a sparse adjoint primitive that exploits the structure of the masking objective to reduce backward pass complexity. BoE achieves a superior Pareto frontier for inference-time scaling compared to existing unmasking methods, demonstrating that gradient-guided steering offers a mathematically principled and efficient path to robust non-autoregressive generation. We will release the code.

翻译：掩码扩散模型（MDMs）已成为生成任务中一种有前景的非自回归范式，具备并行解码和双向上下文利用能力。然而，当前采样方法依赖简单的基于置信度的启发式策略，忽略了局部决策的长期影响，导致轨迹锁定问题——早期幻觉会级联引发全局不一致性。尽管基于搜索的方法能缓解此问题，但其计算成本过高（每步需$O(K)$次前向传播）。本工作提出熵反向引导（BoE），一种梯度引导的推理框架，通过单次反向传播近似无限时域前瞻。我们从轨迹代价函数的一阶展开中形式化推导出令牌影响分数（TIS），证明未来熵对输入嵌入的梯度可作为最小化不确定性的最优控制信号。为确保可扩展性，我们引入\texttt{ActiveQueryAttention}——一种稀疏伴随算子，利用掩码目标的结构特性降低反向传播复杂度。与现有解掩码方法相比，BoE在推理时间缩放方面实现了更优的帕累托前沿，证明梯度引导的引导机制为鲁棒的非自回归生成提供了数学原理严谨且高效的路径。代码将公开。