No controversy between the two sides taken collectively; the divide runs through each school
Between the Protestants taken as a whole and the Roman School taken as a whole there is no dispute at all on this point, although within each school theologians argue over the sense in which man, once grace is given, can act and not act.
Many in the Roman School hold that, whatever helps of grace are given, man can act well and not act in such a way that this is true in the composite sense too, not only in the divided sense. In other words, there is no help of grace whose effect a man may not sometimes block by his defiance and frustrate. Many Protestants hold and profess the same: all the theologians of the Augsburg Confession, and also those called Remonstrants.
Those specifically called Reformed disagree with them here. Their doctrine is that every help of grace necessary and prerequisite for a man's actual conversion always takes effect, and that it infallibly overcomes all the defiance and resistance of the human heart.
In the same way the Roman School has not a few who agree with the Reformed on this point in substance and part company with the other Roman theologians. They teach that divine grace is so effective in itself that it determines the sinner's free choice to good unswervingly and irresistibly, though it does not take away his power to dissent and act otherwise. Among them are not only Jansenius and his disciples but also the so-called later Thomists, such as Diego Alvarez and William Estius.
Latin
LII. Nam inter Protestantes collective consideratos, & Scholam Romanam etiam collective consideratam, nulla prorsus est ea de re controversia, quanquam in utraque Schola disputetur inter Theologos, quo sensu homo, posita gratia, possit operari & non operari. Sunt enim in Schola Romana plurimi qui, positis quibusvis gratiae auxiliis, volunt hominem sic posse bene operari, & non operari, ut id verum sit etiam in sensu composito, non solum in sensu diviso: hoc est, qui volunt nulla esse gratiae auxilia, quorum effectum homo contumacia sua aliquando non impediat, & effectu suo frustretur: Et inter Protestantes plurimi quoque idem sentiunt atque profitentur, nempe omnes Theologi Confessionis Augustanae, & etiam qui Remonstrantes dicuntur. Ac quemadmodum in eo ab iis dissentiunt qui singulariter dicuntur Reformati, quorum doctrina est, omnia gratiae auxilia ad actualem hominis conversionem necessaria & praerequisita nunquam suo effectu carere, sed omnem cordis humani contumaciam & resistentiam infallibiliter ab illis superari: sic quoque in Schola Romana reperiuntur non pauci qui idem, quoad summam rei, cum Reformatis hac in parte sentiunt, & dissident a reliquis Scholae Romanae Theologis; Ac docent gratiam divinam sic per se efficacem esse, ut liberum hominis peccatoris arbitrium ad bonum determinet indeclinabiliter & insuperabiliter, quamvis ab eo non tollat potestatem dissentiendi, & aliter agendi. Quo de numero sunt non tantum Jansenius & ejus discipuli, sed etiam qui dicuntur Thomistae recentiores, ut Didacus Alvares, & Gulielmus Estius.