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High-quality, diverse, and photorealistic images can now be generated by unconditional GANs (e.g., StyleGAN). However, limited options exist to control the generation process using (semantic) attributes, while still preserving the quality of the output. Further, due to the entangled nature of the GAN latent space, performing edits along one attribute can easily result in unwanted changes along other attributes. In this paper, in the context of conditional exploration of entangled latent spaces, we investigate the two sub-problems of attribute-conditioned sampling and attribute-controlled editing. We present StyleFlow as a simple, effective, and robust solution to both the sub-problems by formulating conditional exploration as an instance of conditional continuous normalizing flows in the GAN latent space conditioned by attribute features. We evaluate our method using the face and the car latent space of StyleGAN, and demonstrate fine-grained disentangled edits along various attributes on both real photographs and StyleGAN generated images. For example, for faces, we vary camera pose, illumination variation, expression, facial hair, gender, and age. Finally, via extensive qualitative and quantitative comparisons, we demonstrate the superiority of StyleFlow to other concurrent works.