Generative training has been demonstrated to be powerful for building visual-language models. However, on zero-shot discriminative benchmarks, there is still a performance gap between models trained with generative and discriminative objectives. In this paper, we aim to narrow this gap by improving the efficacy of generative training on classification tasks, without any finetuning processes or additional modules. Specifically, we focus on narrowing the gap between the generative captioner and the CLIP classifier. We begin by analysing the predictions made by the captioner and classifier and observe that the caption generation inherits the distribution bias from the language model trained with pure text modality, making it less grounded on the visual signal. To tackle this problem, we redesign the scoring objective for the captioner to alleviate the distributional bias and focus on measuring the gain of information brought by the visual inputs. We further design a generative training objective to match the evaluation objective. We name our model trained and evaluated from the novel procedures as Information Gain (IG) captioner. We pretrain the models on the public Laion-5B dataset and perform a series of discriminative evaluations. For the zero-shot classification on ImageNet, IG captioner achieves >18% improvements over the standard captioner, achieving comparable performances with the CLIP classifier. IG captioner also demonstrated strong performance on zero-shot image-text retrieval tasks on MSCOCO and Flickr30K. We hope this paper inspires further research towards unifying generative and discriminative training procedures for visual-language models.