15. A non-transitory computer-readable storage medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform operations, the operations comprising: outputting, via a presence-sensitive display device, a graphical keyboard comprising a plurality of keys associated with characters of a first alphabet of a first language, receiving a user input comprising one or more touches on the presence-sensitive display device, constructing a character lattice corresponding to the user input based on a spatial model, the character lattice being indicative of a spatial probability of one or more potential characters corresponding to the user input, constructing a token lattice corresponding to the user input based on the character lattice, the token lattice being indicative of a collective spatial probability of one or more potential tokens corresponding to the user input, wherein each of the one or more potential tokens corresponds to a character candidate string comprising a group of characters representing a semantic or phonetic unit, constructing a word lattice corresponding to the user input based on the token lattice and a language model, the word lattice being indicative of a probability of one or more potential words corresponding to the user input, the one or more potential words comprising one or more characters of a second alphabet of a second language, selecting at least one particular potential word of the one or more potential words based on the word lattice, and outputting, via the presence-sensitive display device, the at least one particular potential word.
15. A non-transitory computer-readable storage medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform operations, the operations comprising: outputting, via a presence-sensitive display device, a graphical keyboard comprising a plurality of keys associated with characters of a first alphabet of a first language, receiving a user input comprising one or more touches on the presence-sensitive display device, constructing a character lattice corresponding to the user input based on a spatial model, the character lattice being indicative of a spatial probability of one or more potential characters corresponding to the user input, constructing a token lattice corresponding to the user input based on the character lattice, the token lattice being indicative of a collective spatial probability of one or more potential tokens corresponding to the user input, wherein each of the one or more potential tokens corresponds to a character candidate string comprising a group of characters representing a semantic or phonetic unit, constructing a word lattice corresponding to the user input based on the token lattice and a language model, the word lattice being indicative of a probability of one or more potential words corresponding to the user input, the one or more potential words comprising one or more characters of a second alphabet of a second language, selecting at least one particular potential word of the one or more potential words based on the word lattice, and outputting, via the presence-sensitive display device, the at least one particular potential word. 16. The computer-readable storage medium of claim 15 , wherein: each of the one or more touches of the user input is associated with a location of the presence-sensitive display device; the spatial model is configured to determine a likelihood that each of the locations of the one or more touches corresponds to one or more particular potential characters; and constructing the character lattice corresponding to the user input based on the spatial model is based on the likelihoods and the locations.