We address the challenge of generating diverse attack prompts for large language models (LLMs) that elicit harmful behaviors (e.g., insults, sexual content) and are used for safety fine-tuning. Rather than relying on manual prompt engineering, attacker LLMs can be trained with reinforcement learning (RL) to automatically generate such prompts using only a toxicity classifier as a reward. However, capturing a wide range of harmful behaviors is a significant challenge that requires explicit diversity objectives. Existing diversity-seeking RL methods often collapse to limited modes: once high-reward prompts are found, exploration of new regions is discouraged. Inspired by the active learning paradigm that encourages adaptive exploration, we introduce \textit{Active Attacks}, a novel RL-based red-teaming algorithm that adapts its attacks as the victim evolves. By periodically safety fine-tuning the victim LLM with collected attack prompts, rewards in exploited regions diminish, which forces the attacker to seek unexplored vulnerabilities. This process naturally induces an easy-to-hard exploration curriculum, where the attacker progresses beyond easy modes toward increasingly difficult ones. As a result, Active Attacks uncovers a wide range of local attack modes step by step, and their combination achieves wide coverage of the multi-mode distribution. Active Attacks, a simple plug-and-play module that seamlessly integrates into existing RL objectives, unexpectedly outperformed prior RL-based methods -- including GFlowNets, PPO, and REINFORCE -- by improving cross-attack success rates against GFlowNets, the previous state-of-the-art, from 0.07% to 31.28% (a relative gain greater than $400\ \times$) with only a 6% increase in computation. Our code is publicly available \href{https://github.com/dbsxodud-11/active_attacks}{here}.