We address the Individualized continuous treatment effect (ICTE) estimation problem where we predict the effect of any continuous-valued treatment on an individual using observational data. The main challenge in this estimation task is the potential confounding of treatment assignment with an individual's covariates in the training data, whereas during inference ICTE requires prediction on independently sampled treatments. In contrast to prior work that relied on regularizers or unstable GAN training, we advocate the direct approach of augmenting training individuals with independently sampled treatments and inferred counterfactual outcomes. We infer counterfactual outcomes using a two-pronged strategy: a Gradient Interpolation for close-to-observed treatments, and a Gaussian Process based Kernel Smoothing which allows us to downweigh high variance inferences. We evaluate our method on five benchmarks and show that our method outperforms six state-of-the-art methods on the counterfactual estimation error. We analyze the superior performance of our method by showing that (1) our inferred counterfactual responses are more accurate, and (2) adding them to the training data reduces the distributional distance between the confounded training distribution and test distribution where treatment is independent of covariates. Our proposed method is model-agnostic and we show that it improves ICTE accuracy of several existing models.