Tanja Bien

Giries Abu Ayoub, Mario Barbara, Lluís Pastor-Pérez et al.

Discrete diffusion language models can generate text efficiently by updating multiple masked positions in parallel, but this parallelism introduces a quality-latency trade-off. Aggressive decoding may commit mutually dependent tokens too early, while conservative decoding requires many denoising steps. Existing methods address this tension by deciding which tokens are safe to reveal using confidence or dependency criteria. However, avoiding unsafe commits does not necessarily make the remaining masked sequence easy to decode, since uncertain tokens may depend on masked tokens, creating a bottleneck for denoising steps. We propose AXON, a training-free module that can be added on top of existing parallel decoding strategies for diffusion language models. Rather than replacing the base decoder, AXON monitors the remaining uncertain masked tokens and intervenes only when their current state suggests that additional context is needed. It then shifts the criterion from which tokens are safest to reveal to which confident reveals would best support later denoising. AXON selects anchors, confident masked tokens that uncertain positions attend to, using attention, uncertainty, and confidence signals. Experiments on reasoning and code-generation benchmarks across multiple diffusion language models show that AXON improves the quality-latency trade-off of existing parallel decoders, often reducing the number of function evaluations while maintaining or improving accuracy.

Francesco Alesiani, Jonathan Warrell, Tanja Bien et al.

We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of distributions, any desired Boolean formula is compilable into such a circuit representation. Second, by combining atomic guidance scores with posterior probability estimates, we introduce a hybrid guidance approach that bridges classifierguidance and classifier-free guidance, applicable to both compositional logical guidance and standard conditional generation. We demonstrate the effectiveness of our framework on multiple image and protein structure generation tasks.

Samir Darouich, Vinh Tong, Lluís Pastor-Pérez et al.

Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such as rotations in three-dimensional space. Equivariant diffusion and flow matching models can incorporate such invariances effectively, even when trained on a non-invariant empirical distribution, but they typically rely on costly multi-step sampling. Recently, drifting models have emerged as an efficient alternative, enabling single-step generation and achieving state-of-the-art performance in generative modeling tasks. However, we show that drifting models face a symmetry-specific challenge, since an equivariant generator does not generally produce the same drifting field as the one obtained from the symmetrized target distribution. Addressing this issue would require expensive symmetrization of the empirical distribution. To avoid this cost, we propose SymDrift, a framework that makes the drifting field itself symmetry-aware. We introduce two complementary strategies: (i) a symmetrized drift in coordinate space based on optimal alignment, and (ii) a $G$-invariant embedding that removes symmetry ambiguity by construction. Empirically, SymDrift outperforms existing one-shot methods on standard benchmarks for conformer and transition state generation, while remaining competitive with significantly more expensive multi-step approaches. By enabling one-shot inference, SymDrift reduces computational overhead by up to 40$\times$ compared to existing baselines, making it promising for high-throughput applications such as virtual drug screening and large-scale reaction network exploration.