Forward path tracing versus backward path tracing. How may I achieve realistic shading in forward path tracing?

I have a forward path tracer. Essentially, it looks flat:

This is the backward path tracer in comparison:

My question is: How do I get pseudorandom lighting like with the backward path tracer, when the eye ray always hits a light in forward path tracing?

Here is my code for the forward path tracer:

float trace_path_forward2(const vec3 eye, const vec3 direction, const float hue, const float eta) { const vec3 mask = hsv2rgb(vec3(hue, 1.0, 1.0)); const vec3 light_o = get_random_light_pos(50, eye, direction, hue, eta);//getRandomPointOnTriangle(A.pos, B.pos, C.pos); const vec3 light_d = RandomUnitVector(prng_state);//vec3(0);//cosWeightedRandomHemisphereDirection(get_normal_by_light_index(tri_index), prng_state); const float energy = 1.0; int step_count = 0; vec3 step_locations[max_bounces + 2]; vec3 step_directions[max_bounces + 2]; step_locations[step_count] = light_o; step_directions[step_count] = light_d; step_count++; if(false == is_clear_line_of_sight(eye, light_o)) { vec3 o = light_o; vec3 d = light_d; for(int i = 0; i < max_bounces; i++) { traceRayEXT(topLevelAS, gl_RayFlagsOpaqueEXT, 0xff, 0, 0, 0, o, 0.001, d, 10000.0, 0); if(rayPayload.dist == -1) return 0.0; const vec3 hitPos = o + d * rayPayload.dist; o = hitPos + rayPayload.normal * 0.01; d = cosWeightedRandomHemisphereDirection(rayPayload.normal, prng_state); step_locations[step_count] = o; step_directions[step_count] = d; step_count++; if(true == is_clear_line_of_sight(eye, step_locations[step_count - 1])) break; } } step_locations[step_count] = eye; step_directions[step_count] = direction; step_count++; // Reverse the path uint start = 0; uint end = step_count - 1; while(start < end) { vec3 temp = step_locations[start]; step_locations[start] = step_locations[end]; step_locations[end] = temp; temp = step_directions[start]; step_directions[start] = step_directions[end]; step_directions[end] = temp; start++; end--; } for(int i = 1; i < step_count - 1; i++) { step_directions[i] = (step_locations[i + 1] - step_locations[i]); } float ret_colour = 0; float local_colour = energy; float total = 0; for(int i = 0; i < step_count - 1; i++) { vec3 step_o = step_locations[i]; vec3 step_d = step_directions[i]; traceRayEXT(topLevelAS, gl_RayFlagsOpaqueEXT, 0xff, 0, 0, 0, step_o, 0.001, step_d, 10000.0, 0); local_colour *= (rayPayload.color.r*mask.r + rayPayload.color.g*mask.g + rayPayload.color.b*mask.b); total += mask.r; total += mask.g; total += mask.b; if(i == step_count - 2 || (rayPayload.color.r > 1.0 || rayPayload.color.g > 1.0 || rayPayload.color.b > 1.0)) { ret_colour += local_colour; break; } } return ret_colour / total; } 

The code for the backward path tracer is:

float trace_path_backward(const int steps, const vec3 origin, const vec3 direction, const float hue, const float eta) { vec3 o = origin; vec3 d = direction; const float energy = 1; const float caustic_energy = 1;//energy; float ret_colour = 0; float local_colour = energy; float total = 0; bool doing_refraction_caustic = false; const vec3 mask = hsv2rgb(vec3(hue, 1.0, 1.0)); for(int i = 0; i < steps; i++) { const float tmin = 0.001; const float tmax = 10000.0; traceRayEXT(topLevelAS, gl_RayFlagsOpaqueEXT, 0xff, 0, 0, 0, o, tmin, d, tmax, 0); total += mask.r; total += mask.g; total += mask.b; if(doing_refraction_caustic) { local_colour += caustic_energy*(rayPayload.color.r*mask.r + rayPayload.color.g*mask.g + rayPayload.color.b*mask.b); doing_refraction_caustic = false; } else { local_colour *= (rayPayload.color.r*mask.r + rayPayload.color.g*mask.g + rayPayload.color.b*mask.b); } // If hit the sky if(rayPayload.dist == -1.0) { ret_colour += local_colour; break; } // If this is simply the final step // then don't throw away perfectly // good data if(i == steps - 1) { ret_colour += local_colour; break; } // Hit a light if(rayPayload.color.r > 1 || rayPayload.color.g > 1 || rayPayload.color.b > 1) { ret_colour += local_colour; break; } vec3 hitPos = o + d * rayPayload.dist; if(stepAndOutputRNGFloat(prng_state) <= rayPayload.opacity) { RayPayload r = rayPayload; if(rayPayload.subsurface > 0) { vec3 o_subsurface = hitPos - rayPayload.normal * 0.001 + RandomUnitVector(prng_state)*0.001; vec3 d_subsurface = RandomUnitVector(prng_state); traceRayEXT(topLevelAS, gl_RayFlagsOpaqueEXT, 0xff, 0, 0, 0, o_subsurface, tmin, d_subsurface, tmax, 0); total += mask.r; total += mask.g; total += mask.b; local_colour += rayPayload.subsurface*(rayPayload.color.r*mask.r + rayPayload.color.g*mask.g + rayPayload.color.b*mask.b); } if(rayPayload.reflector > 0) { vec3 o_reflect = hitPos + rayPayload.normal * 0.01; vec3 d_reflect = reflect(d, rayPayload.normal); traceRayEXT(topLevelAS, gl_RayFlagsOpaqueEXT, 0xff, 0, 0, 0, o_reflect, tmin, d_reflect, tmax, 0); total += mask.r; total += mask.g; total += mask.b; local_colour += rayPayload.reflector*(rayPayload.color.r*mask.r + rayPayload.color.g*mask.g + rayPayload.color.b*mask.b); } rayPayload = r; vec3 o_scatter = hitPos + rayPayload.normal * 0.01; vec3 d_scatter = cosWeightedRandomHemisphereDirection(rayPayload.normal, prng_state); o = o_scatter; d = d_scatter; } else { doing_refraction_caustic = true; vec3 o_transparent = vec3(0.0); vec3 d_transparent = vec3(0.0); // Incoming if(dot(d, rayPayload.normal) <= 0.0) { o_transparent = hitPos.xyz - rayPayload.normal * 0.01f; d_transparent = refract(d, rayPayload.normal, eta); } else // Outgoing { vec3 temp_dir = refract(d, -rayPayload.normal, 1.0 / eta); if(temp_dir != vec3(0.0)) { o_transparent = hitPos.xyz + rayPayload.normal * 0.01f; d_transparent = mix(temp_dir, RandomUnitVector(prng_state), rayPayload.subsurface);// temp_dir; } else { // Total internal reflection o_transparent = hitPos.xyz - rayPayload.normal * 0.01f; d_transparent = mix(reflect(d, -rayPayload.normal), RandomUnitVector(prng_state), rayPayload.subsurface);//reflect(d, -rayPayload.normal); } } o = o_transparent; d = normalize(d_transparent); } } return ret_colour / total; } 

Any comments or questions are appreciated. I think that I'm missing something that might be obvious to another person. If there's anything that I can add to this question, please let me know.