## 1 Introduction
This provides a deeper understanding of the principal dimensions of audio variations in the synthesizer, and an access to higher-level interactions. _Flows_ (NF) [7] also allow to model highly complex distributions in this latent space. Although the use of VAEs for audio applications has only been scarcely investigated, [PERSON] et al. [8] recently proposed a perceptually regularized VAE that learns a space of audio signals aligned with perceptual ratings via a regularization loss. The resulting space exhibits an organization that is well aligned with perception. Hence, this model appears as a valid candidate to learn an organized audio space. Recently, we introduced a radically novel formulation of audio synthesizer control [9] by formalizing it as the general question of finding an invertible mapping between organized latent spaces, linking the audio space of a synthesizer's capabilities to the space of its parameters. We provided a generic probabilistic formalization and showed that it allows to address simultaneously the tasks of _parameter inference_, _macro-control learning_, and _audio-based preset exploration_ within a single model. To solve this new formulation, we proposed _conditional regression flows_, which map a latent space to any given target space, as depicted in Figure 2. Based on this formulation, _parameter inference_ simply consisted of encoding the audio target to the latent audio space that is mapped to the parameter space. Interestingly, this bypasses the well-known blurriness issue in VAEs as we can generate directly with the synthesizer instead of the decoder. In this paper, we extend the evaluation of our proposal on larger sets of parameters against various baseline models and show its superiority in parameter inference and audio reconstruction. Furthermore, we discuss how our model is able to address the task of automatic _macro-control learning_ that we introduced in Ref. [9] with this increased complexity. As the latent dimensions are continuous and map to the parameter space, they provide a natural way to learn the perceptually most significant macro-parameters. We show that these controls map to smooth, yet non-linear parameters evolution, while remaining perceptually continuous. Hence, this provides a way to learn the compressed and principal dimensions of macro-control in a synthesizer. Furthermore, as our mapping is invertible, we can map synthesis parameters back to the audio space. This allows intuitive _audio-based preset exploration_, where exploring the neighborhood of a preset encoded in the audio space yields similarly sounding patches, yet with largely different parameters. In this paper, we further propose _disentangling flows_ to steer the organization of some of the latent dimensions to match given target distributions. We evaluate the ability of our model to learn these _semantic controls_ by explicitly targeting disentanglement in the latent space of the semantic tags associated to synthesizer presets. We show that, although the model learns to separate the semantic distributions, the corresponding controls are not easily interpretable. Finally, we introduce a real-time implementation of our model in _Ableton Live_ and discuss its potential use in creative applications (All code, supplementary figures, results, and the real-time Max4 Live plugin are available as open-source packages on a supporting webpage: [[https://acids-ircam.github.io/flow_synthesizer/](https://acids-ircam.github.io/flow_synthesizer/)]([https://acids-ircam.github.io/flow_synthesizer/](https://acids-ircam.github.io/flow_synthesizer/))). Figure 2: _Universal synthesizer control_. We learn an organized latent audio space \(\mathbf{z}\) of a synthesizer capabilities with a Variational Auto-Encoder (VAE) parameterized with Normalizing Flow (NF). This space maps to the parameter space \(\mathbf{v}\) through our proposed _regression flow_ and can be further organized with metadata targets \(\mathbf{t}\). This provides sampling and invertible mapping between different spaces.