ggplot2 - plot multiple models on the same plot

Question

I have a list of linear and non-linear models derived from different data sets measuring the same two variables x and y that I would like to plot on the same plot using stat_smooth. This is to be able to easily compare the shape of the relationship between x and y across datasets.

I'm trying to figure out the most effective way to do this. Right now I am considering creating an empty ggplot object and then using some kind of loop or lapply to add sequentially to that object, but this is proving more difficult than I thought. Of course it would be easiest to simply supply the models to ggplot but as far as I know, this is not possible. Any thoughts?

Here is a simple example data set to play with using just two models, one linear and one exponential:

df1=data.frame(x=rnorm(10),y=rnorm(10))
df2=data.frame(x=rnorm(15),y=rnorm(15))

df.list=list(lm(y~x,df1),nls(y~exp(a+b*x),start=list(a=1,b=1),df2))

And two separate example plots:

ggplot(df1,aes(x,y))+stat_smooth(method=lm,se=F)
ggplot(df2,aes(x,y))+stat_smooth(method=nls,formula=y~exp(a+b*x),start=list(a=1,b=1),se=F)

Answer 1

EDIT: Note that the OP changed the question after this answer was posted

Combine the data into a single data frame, with a new column indicating the model, then use ggplot to distinguish between the models:

df1=data.frame(x=rnorm(10),y=rnorm(10))
df2=data.frame(x=rnorm(10),y=rnorm(10))

df1$model <- "A"
df2$model <- "B"

dfc <- rbind(df1, df2)

library(ggplot2)
ggplot(dfc, aes(x, y, group=model)) + geom_point() + stat_smooth(aes(col=model))

This produces: