NAE: Normalizing AutoEncoder

Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks, making them viable alternatives to other methods such as diffusion models. In this work, we further advance the state of Normalizing Flow generative models by introducing iterative TARFlow (iTARFlow). Unlike diffusion models, iTARFlow maintains a fully end-to-end, likelihood-based objective during training. During sampling, it performs autoregressive generation followed by an iterative denoising procedure inspired by diffusion-style methods. Through extensive experiments, we show that iTARFlow achieves competitive performance across ImageNet resolutions of 64, 128, and 256 pixels, demonstrating its potential as a strong generative model and advancing the frontier of Normalizing Flows. In addition, we analyze the characteristic artifacts produced by iTARFlow, offering insights that may shed light on future improvements. Code is available at https://github.com/apple/ml-itarflow.

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose \textit{Flow Advantage-Weighted Rectification} (\textbf{FlowAWR}), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2$\times$ to 5$\times$ convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in $>$4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

Small molecules, crystals, and proteins all reduce to atoms in 3D space, yet their generative pipelines remain fragmented across domains, each with its Small molecules, crystals, and proteins all reduce to atoms in 3D space, yet their generative pipelines remain fragmented across domains, each with its own graph, equivariant, or frame-based architecture. Cross-domain training would mitigate per-domain data scarcity, but direct generation in 3D coordinate space cannot easily handle the heterogeneous structural priors of all three domains, and no prior latent autoencoder is simultaneously lossless and architecturally general across all three. We introduce SinAE, a single-architecture flow-matching autoencoder for molecules, crystals, and proteins, with vanilla Transformer encoder and decoder and no equivariant, graph, or domain-specific operators. Rather than requiring the encoder to capture fine-grained geometry, SinAE shifts the reconstruction burden into an iterative flow-matching decoder, achieving near-lossless reconstruction across domains and reducing reconstruction errors by orders of magnitude relative to prior latent baselines. The same per-token latent supports a standard Diffusion Transformer prior that reaches strong performance on molecular, crystal, and protein generation benchmarks. Joint molecule--crystal training strictly improves both domains, providing direct evidence of cross-domain transfer through a shared atomic latent. Code is available at https://github.com/BlueWhaleLab/SinAE .