SinAE: A Single-Architecture Flow-Matching Autoencoder for Cross-Domain Atomic Systems

In molecular discovery, molecule size is coupled to composition, structure, and other target properties. Yet most 3D generators require molecule size to be specified before generation. Here, we introduce Equivariant-Free Transformer-Autoencoded Latent Flow Matching, a two-stage generative framework that relies entirely on a single fixed-dimensional molecule-level latent representation to generate variable-size molecules. The second-stage flow matching model samples this latent vector, and an autoregressive Transformer decoder then determines molecule size while generating atom types, coordinates, and chemically informative states. Canonical atom ordering and rigid-pose alignment enable standard Transformers without equivariant layers, while joint decoding of molecular geometry and an enriched chemical state enables reliable, deterministic, chemistry-guided graph recovery without requiring a learned dense pairwise bond decoder. The same fixed-dimensional latent supports unconditional and property-conditioned flow matching, while optional property supervision adds an internal ranking readout, with no separate predictor or reference calculations. On PCQM4Mv2, EF-TALFM achieves the highest fraction of molecules that are unique, training-set novel, pass sanitization and PoseBusters sanity checks, 89.4%, compared with 75.6% for UAE-3D and 69.8% for FlowMol. EF-TALFM also achieves higher measured computational throughput for training and sampling. Across ten target HOMO--LUMO gaps, internal ranking doubles the density functional theory (DFT)-verified hit rate within $0.1\,\mathrm{eV}$, while preserving 97% novelty among unique verified hits. These results demonstrate that fixed-dimensional molecule-level generation followed by symmetry-resolved autoregressive realization provides a practical architecture for open-ended and property-directed 3D molecular design.

We consider the setting of Normalizing flows with approximate inverses, an established paradigm spanning both full-dimensional ($d=D$) and bottleneck ($d<D$) settings, and group these models under the term flow autoencoders. We present a theoretical investigation into their training dynamics and prove that the proposed loss used by existing approaches is suboptimal; specifically, both encoder and decoder surrogates must be optimized in alignment with reconstruction loss. Guided by these insights, we propose Normalizing Autoencoder (NAE), which employs a novel conditional loss that aligns the surrogate loss gradient with that of reconstruction loss, directly improving upon the current standard. Extensive experiments across molecule generation, tabular data, and image benchmarks demonstrate that NAE achieves state of the art performance. Our work highlights the importance of loss alignment in flow autoencoders and establishes NAE as a powerful generative framework.

Three-dimensional (3D) molecule generation has been dominated by diffusion models, which achieve strong generation quality but typically require the molecular size to be specified a priori. Recent autoregressive approaches have substantially narrowed the performance gap while naturally supporting variable-length generation and conditioning on partial molecular context. However, balancing unconditional and context-conditioned generation remains challenging. We introduce KRONOS, a latent autoregressive diffusion framework that generates molecules in the latent space of a pre-trained autoencoder, jointly modeling molecular graph topology and geometry, while retaining the flexibility of autoregressive generation. We further introduce a mixed training strategy inspired by Fill-in-the Middle (FIM) paradigm, enabling both unconditional and fragment-conditioned molecular generation within a single left-to-right autoregressive model. Experiments on QM9 and GEOM-Drugs demonstrate that KRONOS achieves leading unconditional generation performance among autoregressive methods, while remaining competitive with diffusion models. Moreover, fragment-conditioned generation is achieved with negligible impact on unconditional generation performance, demonstrating that both generation paradigms can be supported within a single architecture.