Recent advances in diffusion models bring the state-of-the art performance on image generation tasks. However, empirical results on previous research in diffusion models imply that there is an inverse correlation on performances for density estimation and sample generation. This paper analyzes that the inverse correlation arises because density estimation is mostly contributed from small diffusion time, whereas sample generation mainly depends on large diffusion time. However, training score network on both small and large diffusion time is demanding because of the loss imbalance issue. To successfully train the score network on both small and large diffusion time, this paper introduces a training technique, Soft Truncation, that softens the truncation time for every mini-batch update, which is universally applicable to any types of diffusion models. It turns out that Soft Truncation is equivalent to a diffusion model with a general weight, and we prove the variational bound of the general weighted diffusion model. In view of this variational bound, Soft Truncation becomes a natural way to train the score network. In experiments, Soft Truncation achieves the state-of-the-art performance on CIFAR-10, CelebA, CelebA-HQ $256\times 256$, and STL-10 datasets.