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With the continuous scaling of integrated circuit technologies, design for manufacturability (DFM) is becoming more critical, yet more challenging. Alongside, recent advances in machine learning have provided a new computing paradigm with promising applications in VLSI manufacturability. In particular, generative learning - regarded among the most interesting ideas in present-day machine learning - has demonstrated impressive capabilities in a wide range of applications. This paper surveys recent results of using generative learning in VLSI manufacturing modeling and optimization. Specifically, we examine the unique features of generative learning that have been leveraged to improve DFM efficiency in an unprecedented way; hence, paving the way to a new data-driven DFM approach. The state-of-the-art methods are presented, and challenges/opportunities are discussed.