The precise physical process that triggers solar flares is not currently understood. Here we attempt to capture the signature of this mechanism in solar-image data of various wavelengths and use these signatures to predict flaring activity. We do this by developing an algorithm that i) automatically generates features in 5.5 TB of image data taken by the Solar Dynamics Observatory of the solar photosphere, chromosphere, transition region, and corona during the time period between May 2010 and May 2014, ii) combines these features with other features based on flaring history and a physical understanding of putative flaring processes, and iii) classifies these features to predict whether a solar active region will flare within a time period of 𝑇 hours, where 𝑇=2 and 24 . Such an approach may be useful since, at the present time, there are no physical models of flares available for real-time prediction. We find that when optimizing for the True Skill Score (TSS), photospheric vector-magnetic-field data combined with flaring history yields the best performance, and when optimizing for the area under the precision–recall curve, all of the data are helpful. Our model performance yields a TSS of 0.84±0.03 and 0.81±0.03 in the 𝑇=2 - and 24-hour cases, respectively, and a value of 0.13±0.07 and 0.43±0.08 for the area under the precision–recall curve in the 𝑇=2 - and 24-hour cases, respectively. These relatively high scores are competitive with previous attempts at solar prediction, but our different methodology and extreme care in task design and experimental setup provide an independent confirmation of these results. Given the similar values of algorithm performance across various types of models reported in the literature, we conclude that we can expect a certain baseline predictive capacity using these data. We believe that this is the first attempt to predict solar flares using photospheric vector-magnetic field data as well as multiple wavelengths of image data from the chromosphere, transition region, and corona, and it points the way towards greater data integration across diverse sources in future work.