Image generative steganography (GS) generates stego images (for hiding private messages) directly without using cover media. However, existing GS methods are vulnerable to noise distortion. Based on this, this paper proposes a steganography scheme based on dual-branch flow called DBF-GS, which improves the robustness and performance of generated stego images. In this work, we design a novel dual-branch flow (DBF) that consists of several reversible flow steps and a non-invertible CNN-based (convolutional neural network) block. DBF approximates common image distortion operations through CNN-based block, providing auxiliary features to restore hidden data in distorted stego images better. In addition, we explore the impact of changes in latent variables on generated images and introduce adversarial learning for flow-based models to optimize the generation of stego images. Moreover, we propose a two-stage separable training strategy to better couple the modules in the architecture, which reduces the encoding of redundant features and further improves robustness. Experiments show our approach effectively resists noising attacks and steganalysis detection, maintaining high image quality and hiding capacity. Compared to existing methods, DBF-GS demonstrates advantages over image robustness and steganographic security.