Discrete Flow Matching

Vision-Language-Action (VLA) models that encode actions using a discrete tokenization scheme have been widely adopted for robotic manipulation, but existing decoding paradigms remain fundamentally limited. Whether actions are decoded sequentially by autoregressive VLAs or in parallel by discrete diffusion VLAs, once a token is generated, it is typically fixed and cannot be revised in subsequent iterations. Consequently, early token errors cannot be effectively corrected later. We propose DFM-VLA, a discrete flow matching VLA that iteratively refines action tokens. DFM-VLA models a token-level probability velocity field that dynamically updates the full action sequence across refinement iterations. We investigate two approaches to constructing the velocity field: an auxiliary velocity-head formulation and an embedding-guided formulation. To further improve prediction accuracy, we introduce a metric-aligned action tokenizer (MAAT) tailored to the coarse-to-fine nature of DFM, together with a two-stage decoding strategy. Extensive experiments on CALVIN, LIBERO, LIBERO-Plus, and real-world manipulation tasks demonstrate the effectiveness of our approach. Our project is available at https://chris1220313648.github.io/DFM-VLA/.

Mass spectrometry (MS) stands as a cornerstone analytical technique for molecular identification, yet de novo structure elucidation from spectra remains challenging due to the combinatorial complexity of chemical space and the inherent ambiguity of spectral fragmentation patterns. Recent deep learning approaches, including autoregressive sequence models, scaffold-based methods, and graph diffusion models, have made progress. However, diffusion-based generation for this task remains computationally demanding. Meanwhile, discrete flow matching, which has shown strong performance for graph generation, has not yet been explored for spectrum-conditioned structure elucidation. In this work, we introduce FlowMS, the first discrete flow matching framework for spectrum-conditioned de novo molecular generation. FlowMS generates molecular graphs through iterative refinement in probability space, enforcing chemical formula constraints while conditioning on spectral embeddings from a pretrained formula transformer encoder. Notably, it achieves state-of-the-art performance on 5 out of 6 metrics on the NPLIB1 benchmark: 9.15% top-1 accuracy (9.7% relative improvement over DiffMS) and 7.96 top-10 MCES (4.2% improvement over MS-BART). We also visualize the generated molecules, which further demonstrate that FlowMS produces structurally plausible candidates closely resembling ground truth structures. These results establish discrete flow matching as a promising paradigm for mass spectrometry-based structure elucidation in metabolomics and natural product discovery.

Existing insertion-based masked diffusion models that generate sequences by interleaving token insertion with unmasking use fixed schedules that are not dependent on the data. For structured sequences like graphs and molecules, learning data-dependent generation orders can improve generation quality by reducing uncertainty over the action space. We propose LoFlexMDM, an insertion-based masked diffusion model with learnable order dynamics that learns data-dependent insertion and unmasking rates. We generalize the discrete flow matching framework to work with variable-length sequences, propose a tractable schedule parameterization and a training objective for joint training of the generator and the target order dynamics. On De Novo and fragment-constrained molecule generation, LoFlexMDM improves sample quality over FlexMDM by up to 17.5% and 6.7%, respectively. These results show that learning the target generation order can improve insertion-based diffusion models without giving up tractable training. We open source the code at https://github.com/dhruvdcoder/LoFlexMDM.

Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down convergence because the model must be consistent across a large space of possible node permutations. We study this trade-off for graph generative models. Specifically, we start from an equivariant discrete flow-matching model, and relax its equivariance during training via a controllable symmetry modulation scheme based on sinusoidal positional encodings and node permutations. Experiments first show that symmetry-breaking can accelerate early training by providing an easier learning signal, but at the expense of encouraging shortcut solutions that can cause overfitting, where the model repeatedly generates graphs that are duplicates of the training set. On the contrary, properly modulating the symmetry signal can delay overfitting while accelerating convergence, allowing the model to reach stronger performance with $19\%$ of the baseline training epochs.