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We aim for image-based novelty detection. Despite considerable progress, existing models either fail or face a dramatic drop under the so-called "near-distribution" setting, where the differences between normal and anomalous samples are subtle. We first demonstrate existing methods experience up to 20% decrease in performance in the near-distribution setting. Next, we propose to exploit a score-based generative model to produce synthetic near-distribution anomalous data. Our model is then fine-tuned to distinguish such data from the normal samples. We provide a quantitative as well as qualitative evaluation of this strategy, and compare the results with a variety of GAN-based models. Effectiveness of our method for both the near-distribution and standard novelty detection is assessed through extensive experiments on datasets in diverse applications such as medical images, object classification, and quality control. This reveals that our method considerably improves over existing models, and consistently decreases the gap between the near-distribution and standard novelty detection performance. The code repository is available at https://github.com/rohban-lab/FITYMI.