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FM Synthesis is a well-known algorithm used to generate complex timbre from a compact set of design primitives. Typically featuring a MIDI interface, it is usually impractical to control it from an audio source. On the other hand, Differentiable Digital Signal Processing (DDSP) has enabled nuanced audio rendering by Deep Neural Networks (DNNs) that learn to control differentiable synthesis layers from arbitrary sound inputs. The training process involves a corpus of audio for supervision, and spectral reconstruction loss functions. Such functions, while being great to match spectral amplitudes, present a lack of pitch direction which can hinder the joint optimization of the parameters of FM synthesizers. In this paper, we take steps towards enabling continuous control of a well-established FM synthesis architecture from an audio input. Firstly, we discuss a set of design constraints that ease spectral optimization of a differentiable FM synthesizer via a standard reconstruction loss. Next, we present Differentiable DX7 (DDX7), a lightweight architecture for neural FM resynthesis of musical instrument sounds in terms of a compact set of parameters. We train the model on instrument samples extracted from the URMP dataset, and quantitatively demonstrate its comparable audio quality against selected benchmarks.