Diffusion model-based generative image steganography (DM-GIS) is an emerging paradigm that leverages the generative power of diffusion models to conceal secret messages without requiring pre-existing cover images. In this paper, we identify a fundamental trade-off between stego image quality, steganographic security, and extraction reliability within the DM-GIS framework. Drawing on this insight, we propose \textbf{PA-B2G}, a \textbf{P}rovable and \textbf{A}djustable \textbf{B}it-to-\textbf{G}aussian mapping. Theoretically, PA-B2G guarantees the reversible encoding of arbitrary-length bit sequences into pure Gaussian noise; practically, it enables fine-grained control over the balance between image fidelity, security, and extraction accuracy. By integrating PA-B2G with probability-flow ordinary differential equations (PF-ODEs), we establish a theoretically invertible mapping between secret bitstreams and stego images. PA-B2G is model-agnostic and can be seamlessly integrated into mainstream diffusion models without additional training or fine-tuning, making it also suitable for diffusion model watermarking. Extensive experiments validate our theoretical analysis of the inherent DM-GIS trade-offs and demonstrate that our method flexibly supports arbitrary payloads while achieving competitive image quality and security. Furthermore, our method exhibits strong resilience to lossy processing in watermarking applications, highlighting its practical utility.