Auto-bidding, with its strong capability to optimize bidding decisions within dynamic and competitive online environments, has become a pivotal strategy for advertising platforms. Existing approaches typically employ rule-based strategies or Reinforcement Learning (RL) techniques. However, rule-based strategies lack the flexibility to adapt to time-varying market conditions, and RL-based methods struggle to capture essential historical dependencies and observations within Markov Decision Process (MDP) frameworks. Furthermore, these approaches often face challenges in ensuring strategy adaptability across diverse advertising objectives. Additionally, as offline training methods are increasingly adopted to facilitate the deployment and maintenance of stable online strategies, the issues of documented behavioral patterns and behavioral collapse resulting from training on fixed offline datasets become increasingly significant. To address these limitations, this paper introduces a novel offline Generative Auto-bidding framework with Value-Guided Explorations (GAVE). GAVE accommodates various advertising objectives through a score-based Return-To-Go (RTG) module. Moreover, GAVE integrates an action exploration mechanism with an RTG-based evaluation method to explore novel actions while ensuring stability-preserving updates. A learnable value function is also designed to guide the direction of action exploration and mitigate Out-of-Distribution (OOD) problems. Experimental results on two offline datasets and real-world deployments demonstrate that GAVE outperforms state-of-the-art baselines in both offline evaluations and online A/B tests. By applying the core methods of this framework, we proudly secured first place in the NeurIPS 2024 competition, 'AIGB Track: Learning Auto-Bidding Agents with Generative Models'.