To leverage crowd-sourced data to train multi-speaker text-to-speech (TTS) models that can synthesize clean speech for all speakers, it is essential to learn disentangled representations which can independently control the speaker identity and background noise in generated signals. However, learning such representations can be challenging, due to the lack of labels describing the recording conditions of each training example, and the fact that speakers and recording conditions are often correlated, e.g. since users often make many recordings using the same equipment. This paper proposes three components to address this problem by: (1) formulating a conditional generative model with factorized latent variables, (2) using data augmentation to add noise that is not correlated with speaker identity and whose label is known during training, and (3) using adversarial factorization to improve disentanglement. Experimental results demonstrate that the proposed method can disentangle speaker and noise attributes even if they are correlated in the training data, and can be used to consistently synthesize clean speech for all speakers. Ablation studies verify the importance of each proposed component.