fix gradient(nan) when two inputs are equal (#32448)

paddle/fluid/operators/dist_op.h

@@ -167,6 +167,7 @@ static void DistGradFunction(const framework::ExecutionContext& context) {
   auto sign =
       (x_minux_y > static_cast<T>(0)).template cast<T>() * static_cast<T>(1.0) +
       (x_minux_y < static_cast<T>(0)).template cast<T>() * static_cast<T>(-1.0);
+  T epsilon = static_cast<T>(1.0e-10f);
 
   // 1: Lp-norm(z), z = x-y, compute dz
   if (p == 0) {
@@ -189,12 +190,14 @@ static void DistGradFunction(const framework::ExecutionContext& context) {
     // dz = pow(abs(x-y)/out, p-1) * sign(x-y) * dout
     if (platform::is_cpu_place(context.GetPlace())) {
       grad_t.device(place) =
-          (x_minux_y_abs / out_t.broadcast(out_bcast_dims)).pow(p - 1) *
+          (x_minux_y_abs / (out_t + epsilon).broadcast(out_bcast_dims))
+              .pow(p - 1) *
           sign.eval() * out_grad_t.broadcast(out_bcast_dims);
     } else {
       grad_t.device(place) =
-          (x_minux_y_abs / out_t.broadcast(out_bcast_dims)).pow(p - 1) * sign *
-          out_grad_t.broadcast(out_bcast_dims);
+          (x_minux_y_abs / (out_t + epsilon).broadcast(out_bcast_dims))
+              .pow(p - 1) *
+          sign * out_grad_t.broadcast(out_bcast_dims);
     }
   }