The diaphragm is a critical muscle for the respiratory system, responsible for up to 70% of the inspiration effort. Phrenic nerve trauma or neuromuscular disease can generate severe diaphragm dysfunction that ultimately leads to respiratory failure. The current treatment for patients with severe diaphragm dysfunction is permanent airway tethering to mechanical ventilation, which greatly impacts patient’s quality of life and autonomy by hindering activities like speech, swallowing, and mobility. Soft robots are ideal to assist in complex biological functions like the contraction of the diaphragm. Diaphragmatic mechanical assistance using implantable soft robots has shown promising results in restoring respiratory function. However, the design of the soft robotic actuator can be optimized to effectively assist the diaphragm. Here, we present a soft robotic pneumatic actuator that inverts its curvature to efficiently displace the diaphragm and assist in the inspiratory effort, restoring physiological thoracic and abdominal pressurization levels. Moreover, we show how the respiratory simulator can replicate clinically relevant pleural pressure and abdominal pressure, demonstrating its potential as a platform to validate this technology.